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Compound interest

Calculate future value and present value using the compound interest formula, and compare compound and simple interest over the same period.

Worked examples

Finding future value using compound interest

Straightforward

Problem

A principal of $3500\$3500 is invested at 4%4\% per annum compound interest for 33 years. Find the future value.

Finding present value given a future value

Moderate

Problem

What principal must be invested at 5%5\% per annum compound interest for 44 years to produce a future value of $6000\$6000? Round to the nearest cent.

Finding the number of years by trying consecutive values

Challenging

Problem

An investment of $4000\$4000 earns compound interest at 6%6\% per annum. After how many complete years will the investment first be worth more than $5000\$5000?

Practise

Q1·Straightforward
Find the future value when $2000\$2000 is invested at 5%5\% per annum compound interest for 33 years.
Q2·Straightforward
A bank account holds $5000\$5000 earning 4%4\% per annum compound interest. Find the balance after 22 years.
Q3·Straightforward
$1500\$1500 is invested at 6%6\% per annum compound interest. Find the future value after 44 years. Round to the nearest cent.
Q4·Straightforward
Find the future value when $10 000\$10\,000 is invested at 3%3\% per annum compound interest for 55 years. Round to the nearest cent.
Q5·Moderate
A sum of $4000\$4000 is invested for 33 years at 5%5\% per annum. By how much does the compound interest earned exceed the simple interest earned over the same period? Round to the nearest cent.
Q6·Moderate
A term deposit will pay $3600\$3600 after 22 years at 4%4\% per annum compound interest. Find the amount that must be deposited now. Round to the nearest cent.
Q7·Moderate
Two options both invest $8000\$8000 for 44 years at 3%3\% per annum: one uses simple interest and one uses compound interest. By how much does the compound interest option produce a higher final value? Round to the nearest cent.
Q8·Moderate
An investment matures to $5000\$5000 after 22 years at 10%10\% per annum compound interest. How much was originally invested? Round to the nearest cent.
Q9·Challenging
$2000\$2000 is invested at 8%8\% per annum compound interest. After how many complete years will the investment first be worth more than $3000\$3000? Find nn by trying consecutive integer values.
Q10·Challenging
Sara can invest $5000\$5000 in Account A at 6%6\% per annum compound interest for 33 years, or Account B at 4%4\% per annum compound interest for 44 years. By how much does the better account's final value exceed the other? Round to the nearest cent.
Q11·Challenging
$3000\$3000 is invested at 10%10\% per annum compound interest. After how many complete years will the investment first be worth more than $4000\$4000? Find nn by trying consecutive integer values.
Q12·Challenging
Two investments both begin with $6000\$6000. Account A earns 5%5\% per annum compound interest for 33 years. Account B earns 3%3\% per annum compound interest for 55 years. By how much does the better account's final value exceed the other? Round to the nearest cent.