1) Helen received an inheritance of $200,000. She invested the entire amount and

Question

1)
Helen received an inheritance of $200,000. She invested the entire amount and expects a yearly return of 10% per annum on her investment and she will receive 150 equal monthly payments. The first payment is expected in 2 years. Find the size of the payments.


2)
An amount of $28,974 is required at the end of 10 years from now, and regular contributions can be made into an investment scheme that pays 8% per annum (compounded annually):

a) What single payment could be made at the beginning of the first year to achieve this objective?

b) What amount could you pay at the end of each year annually, for 10 years to achieve this same objective?

Explanation / Answer

(1)
The value of 200,000 in 2 years at 10% annual rate = 200000*(1+10%)^2 = 200000*1.21
= 242000 = P

PV of the annuity for n =150, A = monthly installment and r = monthly interest rate = (1+10%)^(1/12) = 0.7974%

Installment = P*r/[1-(1+r)-n]

= 242000*0.007974/[1-(1+0.007974)-150]

= 242000*0.007974/[1-(1+0.007974)-150]

= 2771.81

(2)

(a)

FV = PV(1+r)^n

FV = 28974
r = 8%
n =10 years

PV = 28974/(1+8%)^10 = 13420.57

(b)

only 9 annual payments receive interest, last one does not, so n = 9

FV = 28974
r = 8%

FV of 10 payments = FV of first 9 payments + Last payment

FV = A*[1-(1+r)^n]/r + A

28974 = A*[1 - (1+8%)^-9]/0.08 + A

28974 = A*6.24689 + A

A = 3998.13

Should be paid at the end of each year for 10 years.

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