Compounding Annual Interest

Question

Tania deposits $333.33 in a savings account at Bank C each month. The account pays 3.5% annual interest, compounded monthly. How much money, in total, will Tania have after 5 years with Bank C?

Answer 1

The formula for a savings plan with regular deposits is available online or in related textbooks.

A = PMT*[(1+APR/n)^ny -1]/(APR/n). Here PMT is $333.33; APR is 0.035; n = 12 and y = 5

A = 333.33*[1+0.035/12)^12•5-1]/(0.035/12) Follow rules for order of operations.

A = 333.33*[1 + 0.002917)⁶⁰ - 1]/0.002917

A = 333.33*[1.002917)⁶⁰ - 1]/0.002917

A = 333.33*[1.19094 - 1]/0.002917

A = 333.33*[0.19094/0.002917]

A = 333.33*65.4679 = $21,819.00

This compares with $21,885.47 per CalculatorSoup online. The difference is due to rounding and/or the number of decimal places retained during the calculation.

Answer 2

A(5) = 333.33(1 + 0.035/12)^(12)(5)

Can you compute and answer?