Question

Please answer the following questions and submit by due the dates.(20) As part of your retirement planning, you purchase an annuity that pays 4.75% annual interest compounded quarterly.(20.a) If you make quarterly payments of $900 how much will you have saved in 5 years? (20.b). Instead, if you make quarterly payments of $450, how much will you have saved in 10 years?

Answer 1

Given parameters

rate =4.75%

time= 5years

Annuity due refers to a series of equal payments made at the same interval at the beginning of each period. Periods can be monthly, quarterly, semi-annually, annually, or any other defined period.

The formula to be used will be

`FV=P*((1+r)^n-1)/(r)*(1+r)`

From the question given

`\begin{gathered} P=900 \\ n=4*5=20 \\ r=(4.75)/(4)=1.1875\text{ \%}=0.011875 \end{gathered}`

Part A

`900*((1+0.011875)^(20))/(0.011875)*(1+0.011875)`

=> $97112.04

Part B

n=4x10 =40 (Because it is compounded 4 times a year and then for 10 years)

`450*((1+0.011875)^(40))/(0.011875)*(1.011875)`

=>$61486.59