Question

Sectoion 13.3

10. Mrs. Bell expects to retire in 7 years and would like to receive $800 at the end of each month for 10 years following the date of her retirement. How much must Mrs. Bell deposit today in an account paying 7.5% compounded semi-annually to receive the monthly payments?  

Answer 1

we have to calculate the PV.

the monthly payments required is $800.

PMT = $800

N= 10

I/Y = 0.075/2 = 0.0375

the discounting factor/rate per period is (1+ i)^n - 1 = (1.0375)^2 - 1 = 0.0764( since the rate is compounded semi annualy)

the formula for the present value of annuity is:

periodic payment [1 - (1+r)^-n ] /r

THE PRESENT VALUE OF THE AMOUNT IS = 800 * [1 - (1.076)^-10 /0.0764]

=800 * [ 1 - 0.48)/0.0764

= $5445

THE AMOUNT TO BE DEPOSITED TODAY IS $5445.