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# Basic Finance: Annuities, Interest Rates, Rates of Return

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1. Determine the future value of an annuity that pays \$5,000 at the end of the next 11 years. Similar securities pay an interest rate of 7%.

2. How much money would you be willing to pay in order to receive \$800,000 40 years from today? Assume that your required rate of return on investments is 8% compounded semiannually.

3. You are currently making \$300 monthly payments on a \$12,000 7% fixed interest loan that compounds interest monthly. At this rate how long will it take you to repay your loan?

4. You buy a home for \$295,000 with a 15 year fixed mortgage that has an 8.75% interest rate compounded monthly. Determine (1) the monthly payment, and (2) the total interest, principle, and total cash outflow at the end of 1 year.

5. Your friend Jack hires ABC Lawn Service to trim the hedges in his garden. There are three payment options with the company. Which of the following three options should Jack choose if he can earn 8% interest compounded quarterly on his money?
a. Option 1 Pay \$5650 cash immediately
b. Option 2 Pay \$6750 in one lump sum two years from now
c. Option 3 Pay \$800 at the end of each quarter for two years

6. Your boss wants to know which project had a better return. She says that Project Y returned \$7,560 today on a \$2,200 investment three years ago (use annual compounding for Project Y). She also says that Project Z returned \$9,887 today and required investments of \$367 each quarter for the last three years. Which project has a higher return?

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#### Solution Preview

The answers are in the attached file

1. Determine the future value of an annuity that pays \$5,000 at the end of the next 11 year. Similar securities pay an interest rate of 7%.

The question is not very clear. 5000 is paid at the end of next 11 year then that is the future value or if we take annuity value as 5000 per year and find the FV of this annuity at 7% interest. For this purpose we an use the FVIFA table and get the value for 11 years at 7%, this is 15.784 and hence the FV is 5000*15.784= \$78920

2. How much money would you be willing to pay in order to receive \$800,000 40 years from today? Assume that your required rate of return on investments is 8% compounded semiannually.

In this case we are required to find the present value of an investment which will grow to 800,000 in 40 years compounded at the rate of 8% semiannually. We can use the compound interest formula to calculate the present value.
The formula is a s below

CI= P*(1+r/100)n

Where CI is the future value, P is the present value, r is the interest rate and n is the no. of years. In the present case -
CI=800,000, P=?, r=8% and n= 40
Since the compounding is semiannual, we need to divide the interest rate by 2 and multiply the period by 2, we get r=4% and n=80. Putting in the formula we get

800000 = P*(1+0.04)80

solving this equation, P= 800000/(1.04)80 give P = 800000*0.043384
P= 34707.46

3. You are currently making \$300 monthly payments on a \$12,000 7% fixed interest loan that compounds interest monthly. At this rate how long will it take you to repay your loan?

We need to find the number of months required to repay a loan of 12,000 taken at 7% interest ...

#### Solution Summary

The solution explains how to calculate annuities, interest rates and rates of return for time value of money problems

\$2.19