Growing Perpetuity Study Notes

University:
University of Cambridge
Course:
0455 IGCSE | Economics
Academic year:

2023
Views:

105

Pages:

2
Author:

S. Hoovart

economy Corowing Papetuity. In Coeneral. If the interest rate promised by the bank ur you were to put in' to the bank atthe end the first pened and then let your withdraul Conow at a rate of 'g per Anun you Could dothis. Forever. To See explicity Convider that what happens at the end of the Firts peneade: =(1+r)-(. ((1++)-((r-g) === (1+g. T-g T- F-g at the end of the Second pened principal remamingalle 1) (2+1) ہے+r) - c(1+9)=(1+g) (1+r)-((t-g( T-9 c(1+g) = C At the end the third ead the third perned the principal remang willbe c(149) (1+r)-c19): c(1+9)" 5-9 r-g Derivation of the perpetuty Formula ** The present value of a perpetulty is Gavenby + C Now multiply both sides of this equation by C1+r) to get to get: PVC1++) - PV= C + C+C+C (TFT) CI++) (+) 3" - C C C (1+r) (1++)² (1+r)³ C • Simpleying Provides our Result: PVC1++) - PV = C. => PV= C