Question

Nara inherits a perpetuity from her grandfather that will pay here $3000 today and every year forever. The annual interest rate is 4%.

a) How much is Nara's inheritance worth? Nara decides to sell the perpetuity (for its present value) and instead buy an annuity due paying $P for the next 28 years.

b) What is $P? She changes her mind again, and decides instead on an annuity due paying $6000 per year for n years, except for the last (nth) payment which is a drop payment

. c) What is n?

d) What is the amount of the final payment?

Answer 1

Answer (a):

Perpetuity from her grandfather will pay $3000 today and every year forever.

The annual interest rate is 4%

Worth of Nara's inheritance = (3000/4%) + 3000 = $78,000

Worth of Nara's inheritance = $78,000

Answer (b):

PV of annutiy = $78,000

Annuity due for 28 Years

Interest rate = 4%

$P = PMT(rate, nper, pv, fv, type) = PMT(4%,28,-78000,0,1) = $4500.97

$P = $4,500.97

Answer (c):

PMT = $6,000

Number of periods = NPER(rate, pmt, pv, fv, type) = NPER(4%,6000, -78000,0,1) = 17.672988 or 18

n = 18

Answer (d):

Period for finanal payment is = 17.672988 - 17 = 0.672988

Amount of final payment = PV(rate, nper, pmt, fv, type) = PV(4%,0.672988, -6000,0,1) = $4063.76

Amount of final payment = $4,063.76