# annual rate

1.Find the compound amount if $6,400 is invested for 2 years at 12% compounded monthly. What difference would compounding daily make in this example?

2.Deposits of $1,000, $1,100 and $680 were made into a savings account, the first two years ago, the second 18 months ago, the third 6 months ago. How much is in the account now if the interest on all deposits is 12% compounded semi-annually?

3.A deposit of $2,000 earns interest at a rate of 14% compounded quarterly. After two and a half years the interest rate changes to 13.5% compounded monthly. How much is in the account after six years?

4.Which is a better rate of interest, 16% compounded quarterly or 16 1/4% compounded semi-annually?

5.Billy Burnett's grandfather willed Billy $10,000 payable on his twenty-first birthday. What will be the value of the bequest when Billy reaches 17 years of age if money is worth 8% compounded semi-annually?

6.Suppose you had three different offers for your used car. One person will give you $1,000 right now, another offers $1,200 six months from now and the other offers $1,600 two years from now. If interest is 16% compounded quarterly, which offer is worth the most.

7.At 16% compounded quarterly, how long would it take for money to triple?

8.At what annual nominal rate of interest will $6,900 earn $6,400 interest in five years?

9.You want to have $1,000,000 in your bank account when you turn 65 years old. Today is your 20th birthday. As a birthday present you received $27,000 and you want to invest this amount. At what annual interest rate must you achieve to realize this goal?

#### Solution Preview

1. The annual rate is 12%, then the monthly rate is 12%/12 = 1% = 0.01.

If $6,400 is invested for 2 years compounded monthly, then the final amount is

$6,400 * (1 + 0.01)^24 = $8,126.30

If $6,400 is invested for 2 years compounded daily, then the final amount is

$6,400 * (1 + 0.12/365)^(365 * 2) = $8,135.67

The difference is $8,135.67 - $8,126.30 = $9.37

2. The annual rate is 12%, then the semi-annual rate is 12%/2 = 6% = 0.02.

The final amount of the first deposit is $1,000 * (1 + 0.02)^4 = $1,082.43

The final amount of the ...

#### Solution Summary

Monthly and annual rates are featured.