Question

Tommy and Shan Li established a plan to save $300 per month for their children’s education. Their oldest child is six years old and will begin college in 12 years. They will invest the $300 in a savings account that they expect will earn interest of about 5 percent per year, compounded monthly, over the next 12 years. The Lis wonder how much additional money they would accumulate if they could earn 7 percent a year, compounded monthly, on the savings account instead of 5 percent. They also wonder how their savings would accumulate if they could save $400 per month instead of $300 per month at either of these rates of return. The Lis have asked for you to help them determine the answers to these questions.

Answer 1

They will invest the $300 in a savings account that they expect will earn interest of about 5 percent per year, compounded monthly, over the next 12 years.

Annuity, A = $ 300

Interest rate per annum = 5%; Frequency = Monthly

Interest rate per period = interest rate per month, R = 5% / 12 = 0.42%

Period, N = nos. of months in 12 years = 12 x 12 = 144

Hence, Future Value, FV = (A / R) x [(1 + R)^N - 1] = 300 / 0.42% x [(1 + 0.42%)¹⁴⁴ - 1] = $ 59,029

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The Lis wonder how much additional money they would accumulate if they could earn 7 percent a year, compounded monthly, on the savings account instead of 5 percent.

R now = 7% / 12 = 0.58%

Hence, Future Value, FV = (A / R) x [(1 + R)^N - 1] = 300 / 0.58% x [(1 + 0.58%)¹⁴⁴ - 1] = $ 67,408

Additional money they would accumulate = 67,408 - 59,029 = $ 8,379

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They also wonder how their savings would accumulate if they could save $400 per month instead of $300 per month at either of these rates of return.

A = 400

For 5% annual interest rate, R = 0.42%

Hence, Future Value, FV = (A / R) x [(1 + R)^N - 1] = 400 / 0.42% x [(1 + 0.42%)¹⁴⁴ - 1] = $ 78,705

For 7% annual interest rate, R = 0.58%

Hence, Future Value, FV = (A / R) x [(1 + R)^N - 1] = 400 / 0.58% x [(1 + 0.58%)¹⁴⁴ - 1] = $ 89,878