Question

at age 21 Julio begin saving $800 each year until age 35 in an ordinary annuity paying 5.3% annual interest compounded yearly and then leaves his money in the account until age 35. His friend max begins at age 41 saving $1600 per year in the same type of account until age 65. How much does each have in their account at age 65

Answer 1

Solution:

$A=R\times\dfrac{(1+\frac rm)^n-1}{\frac rm}$

A = accumulated account

R =regular annual payment = 800

r/m= rate of interest=5.3%=0.053

n = number of periods=15

So, $A=800\times\dfrac{(1+0.053)^{15}-1}{0.053}$

$\Rightarrow A=\$17657.8$

So, accumulated amount for 15 years = $ 17657.8

Julio's accumulated amount at the end of 65 years = $17657.8(1.053)^{30}=83135.7$

Max's accumulated amount at the end of 65 years $=2600\times\dfrac{(1+0.053)^{25}-1}{0.053}=\$129348.3$