Finance Answer Note #17

Question 1 A fund donated by a wealthy person to GEP to provide annual scholarship to deserving GE students. The fund will grant P5,000.00 for each, for the first five years, P8,000.00 for the next 5 years and P10,000.00 for each year, thereafter. The scholarship will start one year after the fund is established. If the fund earns 8% interest, what is the amount of the donation? Answer Based on the given information, the wealthy person has set up a fund to provide annual scholarships to deserving GE students with a specific grant amount for the first five years, the next five years, and the remaining years thereafter. The scholarship will only start one year after the fund has been established, implying that the donations will be made in advance to cover the first year of the scholarship. In order to calculate the amount of the donation, we need to determine the present value of the future scholarship grants. This can be done by using the formula for Present Value of an Annuity, which is: P = (R * (1 - (1 + i)^-n)) / i, where: P = present value (amount of donation) R = annual payment or grant amount per year (P5,000.00 for the first five years, P8,000.00 for the next five years, and P10,000.00 thereafter) i = interest rate (8% or 0.08) n = number of years (for the first five years, it is 5; for the next five years, it is 10; and thereafter, it is infinite or can be represented as ∞) Plugging in the values, we get: For the first five years: P = (5,000 * (1 - (1 + 0.08)^-5)) / 0.08 = P18,907.13 For the next five years: P = (8,000 * (1 - (1 + 0.08)^-10)) / 0.08 = P44,021.67 Thereafter: P = (10,000 * (1 - (1 + 0.08)^-∞)) / 0.08 = P125,000.00 Therefore, the total amount of the donation is P18,907.13 + P44,021.67 + P125,000.00 = P187,928.80. Question 2 As an incentive to attract savings deposits, most financial institutions today offer daily and even continuous compounding. This means that savings, or passbook, accounts, as well as certificates of deposit ( CDs ) , earn interest compounded each day or even more frequently, such as every hour or even every minute. ( Continuous compounding, in which compounding occurs every instant, involves a different formula that is derived from the formula we've been using. ) Let's take a look at daily compounding. To calculate the compound amount, A , of an investment with daily compounding, use the compound interest formula modified as follows: Rate per period ( daily ) = i 3 6 5 ( nominal interest rate, i , divided by 3 6 5 ) Number of periods ( days ) , n , = number of days of the investment. A = P 1 + i 3 6 5 n Calculator Sequence: ( 1 + ( i - : 3 6 5 ) ) yx n ✕ P = A . ( Round your answers to the nearest cent. ) On April 1 6 , Thomas Ash deposited $ 2 , 5 0 0 in a passbook savings account at 3 . 5 % interest compounded daily. What is the compound amount ( in $ ) of his account on August 5 ? Using daily compounding, calculate the compound amount ( in $ ) of a $ 7 , 0 0 0 investment for each of the three CDs . The First National Bank is offering a 5 year CD at 4 % interest. The Second National Bank is offering a 5 year CD at 3 % interest. The Third National Bank has a 5 year CD at 5 . 5 % interest. Answer As a college student with high marks, it is important to understand the concept of compound interest and how it affects savings and investment accounts. In the question given, we are presented with a scenario and a series of calculations to determine the compound amount of investments with daily compounding. It is crucial to follow the correct formula and steps to accurately calculate these amounts. To start, let's look at the formula provided: A = P 1+ i365n. This means that the compound amount (A) of an investment is equal to the principal amount (P) multiplied by the quantity of 1 plus the rate per period (i365) raised to the power of the number of periods (n). The rate per period in daily compounding can be found by dividing the nominal interest rate (i) by 365, as shown in the formula. In the given problem, we are asked to calculate the compound amount of Thomas Ash's passbook savings account on August 5, using daily compounding. With a starting deposit of $2,500 and an interest rate of 3.5%, we can first find the rate per period by dividing 3.5% by 365, which gives us an i365 of 0.009589. Next, we need to find the number of periods (n), which is the number of days from April 16 to August 5, which is 111 days. Now, we can plug these numbers into the formula as follows: A = $2,500 (1+0.009589)111 A = $2,500 (1.009589)^111 A = $2,500 (1.095149) A = $2,737.87 This means that the compound amount of Thomas Ash's account on August 5 is $2,737.87. Moving on to the next part of the question, we are asked to calculate the compound amount of a $7,000 investment for three different CDs with varying interest rates: 4%, 3%, and 5.5%. Again, we will follow the same formula and steps to find the compound amount for each investment. For the 4% CD, we would have a rate per period of 0.010959 (4% divided by 365) and a number of periods (n) of 1,825 (5 years multiplied by 365 days). Plugging these numbers into the formula, we get a compound amount of $8,325.81. For the 3% CD, we would have a rate per period of 0.008219 (3% divided by 365) and a number of periods (n) of 1,825 (5 years multiplied by 365 days). This would give us a compound amount of $7,674.01. Lastly, for the 5.5% CD, we would have a rate per period of 0.015068 (5.5% divided by 365) and a number of periods (n) of 1,825 (5 years multiplied by 365 days). The compound amount for this investment would be $9,265.42. In conclusion, as an ambitious college student, it is vital to understand and apply financial concepts such as compound interest in everyday situations. With proper knowledge and calculation skills, we can make informed decisions on where to invest our money and maximize our savings. Question 3 in planning for your retirement you would like to withdraw $50000 per year for 15 years . the first withdrawal will occur 20 years from today . what amount must you invest today if your return is 15% per year Answer In order to accurately determine the amount that one must invest today for a 15% return per year in order to withdraw $50000 per year for 15 years, some calculations must be done. First, we must consider the time value of money and the concept of compounding interest. Time value of money states that the value of money today is worth more than the same amount in the future, due to the potential for earning interest over time. Compounding interest refers to the practice of earning interest on both the initial investment and the accumulated interest from previous periods. To calculate the required investment amount, we can use the present value of an annuity formula, which is: PV = Pmt x [(1 - (1 + r)^-n)/r], where PV is the present value, Pmt is the annual payment, r is the interest rate, and n is the number of years. Substituting the given values in the formula, we get: PV = $50000 x [(1 - (1.15)^15)/0.15] = $323,660.12. This means that the total amount that must be invested today at a 15% return is $323,660.12. Alternatively, we can also use the present value of a single sum formula, which is: PV = FV/(1 + r)^n, where FV is the future value, r is the interest rate, and n is the number of years. Substituting the given values in the formula, we get: PV = $50000/(1.15)^20 = $258,727.30. This means that the total amount that must be invested today at a 15% return is $258,727.30. Both methods provide slightly different results, but they are close enough to each other to give us a good estimate of the required investment amount. Question 4 Assume that you are going to ignore dividends and instead rely on Buffett’s look-through earnings to represent a firm’s current and expected cash flow. The tax rate on dividends is 30%. Current earnings per share are $6.50 and the firm’s earnings are expected to grow by 3% in perpetuity. The market capitalization rate is 8% What is the value of the stock? Write your answer to the nearest dollar without the dollar sign (XX). Answer To calculate the value of the stock using Buffett's look-through earnings approach, we first need to understand the concept of look-through earnings. Look-through earnings is a measure of a company's earnings that includes not only the reported net income but also the retained earnings and the earnings of the company's investments in other companies. This approach is used by legendary investor Warren Buffett to assess the true value of a company's stock. To calculate the value of the stock, we can use the following formula: P = (E x (1 - t) / R) x (1 + g) Where: P = Stock price E = Current earnings per share t = Tax rate on dividends R = Market capitalization rate g = Expected growth rate in perpetuity Substituting the values given in the question, we get: P = ($6.50 x (1-0.30) / 0.08) x (1 + 0.03) P = $4.55 / 0.08 x 1.03 P = $56.66 Therefore, the value of the stock based on Buffett's look-through earnings approach is $56.66. Question 5 create 5 research titles that is similar to this "Quantitative Study on the Impact of Allowance Management on Senior High School Student Expenses at Notre Dame of Bongao" Answer Parental involvement has long been recognized as a key factor in a child's academic success. This quantitative study aims to examine the impact of parental involvement on the academic performance of elementary school students in public schools across the United States. Specifically, the study will focus on the level of parental involvement and its correlation with students' grades, standardized test scores, and overall academic achievement. This study will be conducted using a random sample of elementary school students from various public schools in the United States. Surveys will be distributed to both students and their parents to gather data on the level of parental involvement in their academic lives, as well as students' academic performance. Data analysis will be conducted using statistical methods such as regression analysis and ANOVA to determine the correlation between parental involvement and academic performance.