Question

1. You take out a $25,000 30 years mortgage with monthly payments and a rate of 3.5%, monthly compounded. What is your monthly mortgage payment?
2. You take out a $25,000 30 years mortgage with monthly payments and a rate of 3.5%, monthly compounded. What is the loan balance by the end of year 15?
3. Calculate the future value at the end of year 4 of an investment fund earning 7% annual interest and funded with the following end-of-year deposits: $1,500 in at the end of year1, $2,000 at the end of year 2, and $2,500 at the end of year 3, $3,000 at the end of year 4.
4. A company just decided to save $5,500 a month for the next 6 years as a safety net for recessionary periods. The money will be set aside in a separate savings account which pay 4.5% interest compounded monthly. The first deposit will be made today. What would today’s deposit amount have to be if the firm opted for one lump sum deposit today that would yield the same amount of savings as the monthly deposits after 6 years?

Answer 1

Answer to Question 1:

Amount Borrowed = $25,000
Time Period = 30 years or 360 months

Annual Interest Rate = 3.50%
Monthly Interest Rate = 3.50% / 12
Monthly Interest Rate = 0.291667%

Let Monthly Payment be $x

$25,000 = $x/1.00291667 + $x/1.00291667^2 + … + $x/1.00291667^359 + $x/1.00291667^360
$25,000 = $x * (1 - (1/1.00291667)^360) / 0.00291667
$25,000 = $x * 222.694874
$x = $112.26

Monthly Payment = $112.26

Answer to Question 2:

Remaining Period = 15 years or 180 months

Loan Outstanding = $112.26/1.00291667 + $112.26/1.00291667^2 + … + $112.26/1.00291667^179 + $112.26/1.00291667^180
Loan Outstanding = $112.26 * (1 - (1/1.00291667)^180) / 0.00291667
Loan Outstanding = $112.26 * 139.883081
Loan Outstanding = $15,703.27