# Worksheet on Variable Rate of Compound Interest

Practice the questions given in the worksheet on variable rate of compound interest.

If the rates of compound interest for successive years be (r $$_{1}$$%, r $$_{2}$$%, r $$_{3}$$%, r $$_{4}$$%, .................. ) then:

A = P( 1 + $$\frac{r_{1}}{100}$$)(1 + $$\frac{r_{2}}{100}$$)(1 + $$\frac{r_{3}}{100}$$) .............

Where,

A = amount;

P = principal;

r $$_{1}$$, r $$_{2}$$, r $$_{3}$$, r $$_{4}$$.......... = rates for consecutive years.

1. What principal will amount to $9,856 in two years, if the rates of interest for successive years are 10% and 12% respectively? 2. A sum of$ 4,000 is invested at 8% compound interest for the first year and 10% for the second year. Find the amount after 2 years.

3. If the rates of compound interest for the first and the second year be 7% and 8% respectively, then find the compound interest on $6000 for 2 years. 4. Calculate the amount and the compound interest on$ 7,500 is 2 years when the rates of interest for successive years are 8% and 10% respectively.

5. What sum of money will amount to $5,724 in 2 years if the compound interest rates are 6% and 8% for successive years? 6. Calculate the compound interest accrued on$ 6,000 in 3 years, compounded yearly, if the rates for the successive years are 5%, 8% and 10% respectively.

7. If the rates of compound interest for the first and the second year be 8% and 7% respectively, then find the compound interest on $6000 for 2 years. 8. Calculate the amount of$ 15,000 in 2 years, compounded annually, if the rates for the successive years are 8% and 10% respectively.

9. Calculate the amount and the compound interest on $12,500 is 3 years when the rates of interest for successive years are 8%, 10% and 10% respectively. 10. A sum of$ 40,000 is invested at 10% per annum compound interest for 3 years. In the first two years the interest is reckoned yearly and then it is reckoned half-yearly. Find the amount after 3 years.

11. On a certain sum, the compound interest in 3 years amounts to $4,453.20. If the rates of interest for successive years are 5%, 8% and 10% respectively, find the sum. 12. A sum of$ 5,000 is lent for 3 years at compound interest. If the rates of interest for the successive years are 10%, 12% and 15% respectively, find the difference between the compound interest for the first year and the compound interest for the third year.

Answers for the worksheet on variable rate of compound interest are given below.

1. $8,000 2.$ 4,752

3. $933.60 4.$ 8,910

5. $5,000 6.$ 1,484.40

7. $933.60 8.$ 17,820

9. 1,410

10. $53,361 11.$ 18,000

12. \$ 424

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