# Multiple interest period deposits

When interest is added to capital, the amount of increased capital is obtained by multiplying the capital by the interest factor.

Example 1.

A deposit of €500 is made to an account. The interest rate on the account is 1,5%. How much money is in the account after a year?

The interest factor is 1,015.

If the capital increases in interest over several years, then the amount of the increased capital is obtained by successive multiplications.

Example 2.

A deposit of €500 is made to an account. The interest rate on the account is 1,5%. How much money is in the account after three years?

Note that the multiplication can also be denoted by a power notation:

This phenomenon is called interest on interest. (compound interest)

As a general method of calculating interest on interest

Example 3.

Liisi deposits €10 000 in a five-year fixed-term account. How big does the deposit increase when the interest rate on the account is 2,5% and interest is added onto the account at the end of each year?

This same “formula” can be used to determine other components of a question.

Example 4.

Liisi deposits €4500 for six years. The capital will increase to €5470 during this period. What is the interest rate on the account?

The interest rate on the account is 3,3%.

Example 5.

A four-year time deposit was made to an account with an interest rate of 2,6%. After four years, €1662,20 could be withdrawn from the account. How big was the deposit made to the account?

The deposit was €1500.

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### Exercises

1. What is the interest rate factor if the account interest rate is 1,7%?

A) 1,017

B) 0,017

C) 1,17

D) 1,0017

2. €1000 is deposited into an account for three years. The interest rate on the account is 2,5%. What expression can you use to calculate how much money is in your account, three years after the deposit?

A) 1000 · 1.0025³

B) 1000 · 1.025³

C) 1000 · 1.25³

D) 1.0025 · 1000 · 3

3. €1825 is deposited into an account with an interest rate of 3,25%. How much could be withdrawn from the account after five years?

4. €125 was deposited into an account. What was the interest rate on the account when €13148 could be withdrawn from the account at the end of a three-year deposit period?

5. €1500 will be deposited into an investment account. Form an equation that can be used to calculate the interest rate of the account when the account has €1580 after five years.

6. €1500 will be deposited into an account for a year. The interest rate on the account is 1.5%.

a) How much interest is paid on the account?

b) Income from the interest on deposits is taxable income. The tax payable on this interest is called 'tax at source on interest', and is at 30%. How much tax at source on interest is paid from the interest?

7. The net interest rate means the actual interest rate paid on a deposit. The net interest rate is obtained when the tax at source on interest (30%) is deducted from the interest rate paid by the bank. The interest rate on the account is 1,5%. The net interest rate can be calculated

A) 1.5 · 0.3

B) 1.5 · 0.7

C) 1.5 - 0.3

D) 1.015 · 0.7

8. €1250 will be deposited into an investment account for one year. The interest rate on the account is 1,6%. What is the net interest paid on the account when the tax at source on interest is 30%?

9. €1250 will be deposited into an investment account for one year. How much money is in the account after one year when the interest rate on the account is 2,00%?

10. How much had been deposited into an account when €19896 could be withdrawn from the account after a deposit period of five years? The interest rate on the account is 2,6%. Tax at source on interest is not taken into account.