Question

26. You can invest in an account that pays simple interest or an account that pays compound interest. In either case, you plan to invest $3,900 today and both accounts have an annual interest rate of 5 percent. How much more interest will you receive in the 11th year in the account that pays compound interest?

27. You want to buy a house and will need to borrow $240,000. The interest rate on your loan is 5.71 percent compounded monthly and the loan is for 25 years. What are your monthly mortgage payments?

Answer 1

Answer 26

Calculation of interest paid in 11th Year using Compound interest

Interest paid in 11th Year using Compound Interest = Value of Investment at the end of 10th year x Interest rate

Value of investment at the end of 10th year = P x (1+r)^n where P = original investment,r = interest rate and n = number of years

Value of investment at the end of 10th year = $3900 x (1+0.05)^10 = $6,352.69

Interest paid in 11th Year using Compound Interest = $6,352.69 x 5% = $317.63

Calculation of interest paid in 11th Year using Simple interest

Interest paid in 11th Year using Simple Interest = Value of original Investment at the end of 10th year x Interest rate

Interest paid in 11th Year using Simple Interest = $3900 x 5% = $195.00

Amount of more interest that you will receive in 11th year = $317.63 - $195 = $122.63

Answer 27

We can use the present value of annuity formula to calculate the monthly mortgage payment.

Present value of annuity = P x {[1 - (1+r)^-n]/r}

Present value of annuity = loan borrowed = $240000

P = monthly mortgage payment = ?

r = interest rate per month = 5.71%/12 = 0.004758

n = number of monthly payments = 25 years x 12 = 300

240000 = P x {[1 - (1+0.004758)^-300]/0.004758}

240000 = P x 159.5682

P = 1504.06

Monthly Mortgage payment = $1,504.06