Question

You have applied for a job with a local bank. As part of its evaluation process, you must take an examination of the time value of money analysis covering the following questions. Please show your work. (Identify N, I/Y, PV, PMT, and FV)

1. Your client is 40 years old; and she wants to begin saving for retirement, with the first payment to come one year from now. She can save $5,000 per year; and you advise her to invest it in the stock market, which you expect to provide an average return of 9% in the future. If she follows your advice, how much money will she have at 65?
2. You have $50,000 to put as a down payment on a new house that cost $350,000, and you have been quoted the following terms: 5% Annual Percentage Rate (APR), for 30 years. If you decide to purchase this home, what will your monthly payment be? Additionally, over the life of the loan what would your total interest expense be?

Answer 1

1]

I/Y = 9 (average rate of return per year)

N = 25 (number of payments from age 41 to 65 is 25 payments)

PMT = -5000 (Yearly payment. This is entered with a negative sign because it is a payment)

PV = 0 (amount currently saved is zero)

CPT --> FV

FV is calculated to be $423,504.48

2]

I/Y = 0.416667 (Monthly rate = annual rate / 12 = 5 / 12)

N = 360 (total number of monthly payments = number of years * 12 = 30 * 12 = 360)

PV = 300000 (loan amount = cost of house - down payment = 350,000 - 50,000 = 300,000)

FV = 0 (loan balance outstanding at end of 30 years is zero)

CPT -->> PMT

PMT is calculated to be $1,610.46

The monthly payment is $1,610.46

total interest expense = (monthly payment * total number of monthly payments) - loan amount

total interest expense = ($1,610.46 * 360) - $300,000

total interest expense = $279,767.35