Question

You deposit $500 today into a savings plan and deposit an additional $50 each quarter (starting in 3 months) for 25 years. If you earn 6.25% compounded quarterly, what will your balance be in 25 years?

Answer 1

Initial deposit = $500
Quarterly deposit = $50
Period = 25 years or 100 quarters
Annual interest rate = 6.25%
Quarterly interest rate = 1.5625%

Accumulated sum = $500*1.015625^100 + $50*1.015625^99 + $50*1.015625^98 + ... + $50*1.015625 + $50
Accumulated sum = $500 * 1.015625^100 + $50 * (1.015625^100 - 1) / 0.015625
Accumulated sum = $500 * 4.713443 + $50 * 237.660356
Accumulated sum = $14,239.74

So, you balance after 25 years is $14,239.74