Question

3. Assume you borrow $100,000 to purchase a house and the stated interest rate is 5 percent. The loan will be set up as an installment loan with monthly payments. What is the annual percentage rate? Show all work to be eligible for full credit. Discuss why the annual percentage rate is different than the stated interest rate.

Answer 1

If the loan is set for monthly payments with 5% annual interest. The real interest you will pay will be higher than 5% due to compounding

By using this formula we can assess the future value of the loan

=100,000*(1+(5/12)%)^(12) = 105,116.19

Interest rate = (105,116.19-100,000)/100,000 = 5.12%

5% interest on $100,000 = $5,000

5% interest on $100,000 after a month = $100,000*(5/12)%

= 417 (This is the interest rate of first month, which is added for payment of next month)

Interest accrues next month will be on 100,000+417 = 100417

= $100,417*(5/12)%

= $418.40

For next month this too will be added to put interest on

= 100,835.07*(5/12)%

= 420.146125

And so on...

To calculate the interest after 1 year the following formula can be used

Future value = present value(1+interest rate per month)^(time in months)

For 1 year

=100,000*(1+(5/12)%)^(12) = 105,116.19

For 2 years

= 100,000*(1+(5/12)%)^(12*2) = 110,494.13

and so on..