Question

John borrows $10,000 for 10 years at an effective interest rate of 10%. He can repay the loan using the amortization method with payments of $1,627.45 at the end of each year. Instead John repays the loan using a sinking fund that pays an annual effective rate of 14%. Deposits to the sinking fund are equal to $1,627.45 less interest on the loan, and are made at the end of each year for 10 years. What is the balance in the Sinking Fund immediately after repayment of the loan?

Answer 1

Answer:

The balance in the Sinking Fund immediately after repayment of the loan will be $2,133.19

Explanation:

Hi, John will pay the loan by paying the yearly interest and the rest is going to go to the sinking fund, so, if he has $1,627.45 and the annual interest of the loan are $1,000, he will be depositing $627.45 into the sinking fund for ten years. Therefore, the future value of the annual deposits of the sinking can be found by using the following formula.

$FutureValue=\frac{A((1+r)^{n} -1)}{r}$

Where:

A = equal annual savings into the sinking fund (that is $627.45)

r = effective rate of the sinking fund (14%)

n = 10 years

Everything should look like this.

$FutureValue=\frac{627.45((1+0.14)^{10} -1)}{0.14}$

$Future Value=12,133.19$

Now, this is the balance after 10 years, but remember that John has to pay the loan, which is $10,000 (not $11,000 because John pays the interest of the loan and then deposits the balance into the sinking fund). Therefore, the balance after repaying the loan is $12,133.19 - $10,000 = $2,133.19.

Best of luck.