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# What is the formula for compound interest questions?

2 years ago

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3 Replies

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Giuseppe Roob

William M Verified Sherpa Tutor ✓

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Hi there. This depends on your question but the default formula is 'starting amount x (1+ or -percentage/100)^n(number of years). For example if the question was:

'how much money would be in a bank account starting at £10,000 offering an interest rate of 1% after 3 years' the formula would be 10000x (1+0.01)^3= £10303.01

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Dawn M

First work out the multiplier. If you are in an increasing situation the multiplier will be 100% plus the % rate, converted into a decimal by dividing by 100. If you are in a decreasing situation the multiplier will be 100% subtract the % rate, converted into a decimal by dividing by 100.

Then to work out the final amount using compound interest, take the initial amount and multiply it by the appropriate multiplier which is raised to the power equal to the number of time periods.

Example: £200 increasing at a rate of 5% for 6 years

Multiplier: 100% + 5% = 105% = 1.05

200 x 1.05 to the power of 6

S
Sinan Eksi

Hi Giuseppe,

Compound interest is calculated using the initial investment, interest rate and duration the investment is compounded over. For example: John invests £2,000 in a bank which has an interest rate of 10%. What will John's investment be worth in 3 years?

In this example, we would take the initial investment of £2000 and multiply it by 1.10 to the power of 3, giving an answer of £2,662. It is the same operation as taking the initial investment of £2000, growing it by 10% by multiplying by 1.10, growing the new number again by 10% by multiplying it by 1.10 and doing so one more time to find the final value after 3 years.

The same operation can be used to calculate depreciation. For example: A car with an initial value of £10,000 depreciates at 20% per year. Find the value of the car after 2 years.

For this example we would again take the initial value of £10,000 and multiply it by 0.8 to the power of 2, giving an answer of £6,400. Again this is the same as taking the initial investment of £10000, reducing it by 20% by multiplying by 0.8, then doing so again with the new value to find the final value after two years.

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