Question

What is the future value in 2 years if you invest $150 at the beginning of each month for 10 months starting today at a rate of 3%, compounded quarterly?

Answer 1

Annual interest rate = 3.00% compounded quarterly

Quarterly interest rate = 3.00% / 4
Quarterly interest rate = 0.75%

Effective annual rate = (1 + Quarterly interest rate)^4 - 1
Effective annual rate = (1 + 0.0075)^4 - 1
Effective annual rate = 1.03034 - 1
Effective annual rate = 0.03034 or 3.034%

Monthly interest rate = (1 + Effective annual rate)^(1/12) - 1
Monthly interest rate = (1 + 0.03034)^(1/12) - 1
Monthly interest rate = 1.002494 - 1
Monthly interest rate = 0.002494 or 0.2494%

Monthly deposit = $150
Number of deposits = 10

Deposits are made at the beginning of each month

Future value in 2 years = $150*1.002494^24 + $150*1.002494^23 + …. + $150*1.002494^16 + $150*1.002494^15
Future value in 2 years = $150 * 1.002494^14 * (1.002494^10 + 1.002494^9 + … + 1.002494^2 + 1.002494)
Future value in 2 years = $150 * 1.002494^15 * (1.002494^10 - 1) / 0.002494
Future value in 2 years = $150 * 10.497983
Future value in 2 years = $1,574.70