# Worksheet on Compound Interest when Interest is Compounded Half-Yearly

Practice the questions given in the worksheet on compound interest when interest is compounded half-yearly.

When the interest is compounded half-yearly (two times is a year) the,

A = P(1 + $$\frac{r}{2 × 100}$$)$$^{n × 2}$$

i.e., the rate percent is divided by 2 and the number of years is multiplied by 2.

1. Find the compound interest and the amount on $4,000 at 4% per annum for 1 year when interest is compounded half-yearly. 2. Calculate the amount when sum of$ 4,800 is invested at 8% per annum for 4 years, the compound interest being compounded half-yearly.

Do not use mathematical tables. Use the necessary information from the following:

(1.08)$$^{4}$$ = 1.3605; (1.04)$$^{8}$$ = 1.3686

(1.08)$$^{8}$$ = 1.8509; (1.04)$$^{4}$$ = 1.1699

3. Calculate the compound interest at 8% per annum, compounded half-yearly, on $3,000 for 1$$\frac{1}{2}$$ years. 4. Find the difference between the compound interest compounded yearly and half-yearly on$ 10,000 for 18 months at 10% per annum.

5. Find the compound interest and the amount on $5,000 at the annual interest rate of 8% for 2 years 6 months. 6. A man invests 4 10,000 in a bank for 1 ½ years at the interest rate of 7$$\frac{1}{2}$$% per annum, compounded annually. Find the amount he will receive at the end of the period. 7. Calculate the compound interest on$ 60,000 for 1 year, at 8% per annum, compounded half-yearly.

8. In what time will a sum of $8,000 become$ 9,261 at the interest rate of 10% per annum if the interest is compounded six-monthly?

9. At 4% per annum, find the compound interest on a certain sum of money for 1 year, compounded six-monthly, when the simple interest on this sum of money for 2 years at the rate of interest 4% per annum is $450. 10. Calculate the compound interest on$ 3500 at 6% per annum for 3 years, the interest being compounded half-yearly.

Do not use mathematical tables. Use the necessary information from the following:

(1.06)$$^{3}$$ = 1.191016; (1.03)$$^{3}$$ = 1.092727

(1.06)$$^{6}$$ = 1.418519; (1.03)$$^{6}$$ = 1.194052

Answers for the worksheet on compound interest when interest is compounded half-yearly are given below.

1. $161.60,$ 4161.60

2. $6,569.28 3.$ 374.60

4.$26.25 5.$ 1,065.28, $6,065.28 6.$ 11,153.13

7. $4896 8. 1$$\frac{1}{2}$$ years. 9.$ 227.25

10. \$ 679.18

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