Henry invests $5,000 in a mutual fund with an annual interest rate of 7.5%. He also has a 4-yr, $10,000 loan at 3.75%. When will the amount of interest earned on the mutual fund be equal to the amount of interest paid on the loan?

Question

Henry invests $5,000 in a mutual fund with an annual interest rate of 7.5%.  He also has a 4-yr, $10,000 loan at 3.75%.  When will the amount of interest earned on the mutual fund be equal to the amount of interest paid on the loan?

Henry · Answer

Loan: $10,000 @ 3.75% for 4 years.

Pt = (Po*r*t) / (1 - (1+r)^-t.

r = (3.75% / 12)/100% = 0.003125 =
monthly % rate express as a decimal.

t = 4yrs * 12mo/yr = 48mo.

Pt=(10,000*0.003125*48)/(1-(1.003125)^-48.
Pt = 10784.33.

Int. = 10,784.3 - 10000 = 784.33.

Investment: $5,000 @ 7.5%.

Int. = 5000 * 0.075t = 784.33,
375t = $784.33,
t = 2.09yrs = 25mo.