Question

5) (10%) Calculate the monthly mortgage payment for the following two scenarios. A. $200,000 loan for 15 years at 3%. B. $400,000 loan for 30 years at 4%.

6) (10%) An executive wants to take out $50,000 from her retirement account at the beginning of each year that she is retired. She estimates her account will earn 3% during retirement and she will need to be able to withdraw the funds each year for 25 years. How much money will the executive need to have in her account when she starts retirement?

7) (10%) Continuing the scenario from question 6: The executive will have deposited funds at the beginning of each month into her retirement account for 30 years prior to retirement. The account will have averaged a 9% return. How much money will she need to have deposited each month to reach her retirement balance goal (from question 6)?

Answer 1

5. Calculation of monthly mortgage payment

Monthly mortgage payment = [ P * R * ( 1 + R ) ^ N ] / [ ( 1 + R ) ^ N - 1]

where P = Loan amount

   R = Interest rate per month

   N = No of payments

A. $200,000 loan for 15 years at 3%

Monthly mortgage payment = [ 200000 * (0.03/12) * (1 + [0.03/12] ) ^ (15 * 12) ] / [ ( 1 + [0.03/12] ) ^ (15 * 12) - 1 ]

= ( 200000 * 0.0025 * 1.57 ) / ( 1.57 - 1)

= $ 1377

B. $400,000 loan for 30 years at 4%

Monthly mortgage payment = [ 400000 * (0.04/12) * (1 + [0.04/12] ) ^ (30 * 12) ] / [ ( 1 + [0.04/12] ) ^ (30 * 12) - 1 ]

= ( 400000 * 0.0033 * 3.31 ) / ( 3.31 - 1)

= $ 1892

6. Money will the executive need to have in her account when she starts retirement

Money needed today = Money to be withdrawn * PVIFA (3%, 25 years)

= 50000 * 17.41

= $ 870,500