Compound interest

The formula for compound interest is:

REMEMBER: This calculation provides the total value of the investment -
that is the investment PLUS the interest earned.

When entering the values into your calculator DO NOT change the percentage to a decimal.
Enter it as given in the question and then add the % sign.
The number then is the same as in the question and you do not make an error (often accidental)
in entering a number which is not in the question.

Many people - those who do not understand calculators - will try to make you use decimals.

If the interest is paid at times other than annually, divide the percentage by the number of periods in one year and then multiply the n (number of periods) by that same value - see the calculator displays in the solutions for some of the questions below.

For example:

Questions on this page address:

1. Finding the interest rate.

2. Determining the amount finally received.

3. Determining the interest received.

4. Determining amounts to be invested now.

5. Comparing simple and compound interest.

Interest rate.	1. What % rates are equivalent to 12% p.a. when the period is reduced to: (i) six monthly? (ii) Quarterly? (iii) Monthly? (iv) Daily? Answer.(i) 6% per half year. (ii) 3% p.q. (iii) 1% p.m. (iv) 0.03288% p.d.
	2. What annual percentage rate is equivalent to: (i) 2% per quarter? (ii) 1.5% per month? (iii) 0.0612% per day? Answer.(i) 8% p.a. (ii) 18% p.a. (iii) 22.34%p.a.
Amount received.	3. What is the final value of an investment (to the nearest dollar) if $1,000 is invested for: (i) 5 years at 6% per annum compounded monthly?. (ii) 5 years at 6% per annum compounded half-yearly? Answer.(i) $1,349. (ii) $1,344.
	4. What is the final value of an investment if $5,432 is deposited into an account for 10 years with the 8.25% p.a interest paid quarterly? Answer.Final value is $12,291.58.
	5. A stamp collection was valued at $30,000 at the beginning of 2019. Market analysts consider that it will increase in value by 7.5% p.a. What is the expected increase in the value of the collection by the end of 2022 (to the nearest $100)? Answer.Expected increase is $10,100.
Interest received.	6. Lara invests $7,400 in an account paying 2% p.a. quarterly interest for 3 years. How much interest will she earn? Answer.$456.42.
	7. Lindsay invests $4,000 into an account earning interest at 2.5% p.a., compounded monthly. If she leaves the money in the account for 2 years, how much interest will she earn (to the nearest cent)? Answer.$204.87.
	8. How much interest is paid if $5 million is deposited into a fund for 5 days at a 6% compounding rate payable daily? Answer.$4,110.94.
Present investment amounts.	9. The value of an investment in the future will be $32,000 if the investment attracts a rate of 10% p.a. compounding monthly. What is the present amount (to the nearest $) which has to be deposited to achieve that target? Answer.$19,820.
	10. What amount must be invested now at 4% per annum, compounded quarterly, so that in five years it will have grown to $60,000? Answer.$49,173.
	11. Calculate the present value of an investment which will have a future value in 5 years time of $800,000. Use an interest rate of 8% compounding monthly. (Answer to the nearest $100). Answer.Present value is $537,000.
	12. What amount must be invested now at 5% per annum, compounded monthly, so that in four years the amount will be $50,000? (Answer to the nearest $10). Answer.Present value is $40,950.
	13. What single amount of money (to the nearest $10) would need to be invested today at 5.4% p.a. compounded monthly if, after 3 years, the account had a balance of $10,000? Answer.$8,510.
Simple & compound interest compared.	14. (i) Ashleigh borrows $25,000 as a personal loan. She is charged 8% p.a. interest compounded monthly with a reducible balance. At the end of the first month, Ashleigh repays $3,000. How much is her balance after her first repayment? (ii) Redo the calculation but assume Ashleigh paid 8% p.a. simple interest. Explain this balance in relation to the previous balance. Answer.(i) $456.42.
	15. What is the equivalent simple interest rate p.a. to a compound interest rate of 10% p.a. paid quarterly for 6 years? Hint.Equate the two equations calculating the equivalent interest amounts. Answer.Equivalent rate is 30.15%.
	16. I have a choice of investments for my $1,500 over the next 3 years: Option 1: 4.5% p.a. compound interest; Option 2: 5.5% p.a. simple interest. (i) Which is my better investment and why? Calculate the value of both investments after one year. (ii) What rate of simple interest is the equivalent of the compound interest in Option 1? (iii) If the simple interest in Option 2 was paid at the end of each quarter, what would be the difference in the amount I received from my original annual simple interest investment? Answer.(i) Option 2 yields $1,747.50 against Option 1 giving $1,711.75. (ii) Equivalent rate is 4.71% (iii)No difference.