Answer to Question #116982 in Financial Math for Sandy

Question

A man deposits an amount of Rx into an investment account paying 8,76% p.a. compounded quarterly. Thirty years later he withdraws R50000 from the accumulated amount in the account and immediately invests the remainder in a retirement annuity which earns 9% p.a. The retirement annuity will provide him with a regular monthly income of R25000 for the next fifteen years starting one month after the investment is made. The original amount Rx (to the nearest rand) is equal to

Answer 1

Solution: Find Rx 

Find the present value of the Annuity. 

Pv A= Annuity{1-(1+r)^-n}/r

Pv A= 25000{1-(1+0.09÷12)^-15*12}/0.09÷12

Pv A=25000*{1-(1+0.0075)^-180}/0.0075

Pv A= 25000(98.5934)

Pv A=R2464835

Thus future value of the investment= R 2464835+R 50000

Future value of the investment=R 2514835

To find the original amount find the present value of rhe investment.

Pv=FV*{1÷(1+r)ⁿ}

Pv=FV/(1+r)ⁿ

Pv=2514835÷[(1+0.0876÷4)^30*4]

Pv=2514835÷(1.0219)¹²⁰

Pv=2514835÷13.4588

Pv=186853.66

Rx to the nearest Rand= 186854

=R 186,854