# Basic Finance: Compound Interest, Rate of Return, Annuities

1. Today you borrow $80,000 to finance the purchase of your new sports car. Interest will be 5% compounded monthly. Payments will be made at the beginning of the month. You will repay the loan over 4 years. How much will the payments be?

2 If you borrow $100 and pay back $3600 in 5 years, what annual interest rate are you paying?

3. Find the present value of a $600 payment received at the beginning of every 6 months for 3 years with interest compounded 4% semiannually.

4. You invest $500 at the beginning of each month for 4 years. Interest is 3% compounded monthly. How much is in the account at the end of the four years?

5. Your parents placed $5,000 in a trust fund for you. In 12 years the fund will be worth $10,000. What is the rate of return on the trust fund?

6. Calculate the future value of $7000 4 years from now using a discount rate of 6%. Compound interest quarterly.

7. What is the present value of an annuity that pays $300 semiannually at the beginning of the next 6 years? Use a discount rate of 6%.

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#### Solution Preview

1. Today you borrow $80,000 to finance the purchase of your new sports car. Interest will be 5% compounded monthly. Payments will be made at the beginning of the month. You will repay the loan over 4 years. How much will the payments be?

PV = 80,000

Interest rate = 5% / 12 = 0.4167%

Number of periods = 4*12 = 48

FV = 0

Then by a financial calculator, we can compute payment each period = $1,834.70

You will repay the loan by $1,834.70 each month.

2 If you borrow $100 and pay back $3600 in 5 years, ...