# Calculate Compound Interest: Easy Step-by-Step Guide | Calculator Tips

• MHB
• logicandtruth
In summary, John borrows £500 over 2 years from a building society at a rate of 12% per annum compounded quarterly. The final amount of interest to be paid is 133.38.
logicandtruth
Hi new to the forum and would like to improve my level of maths. I am working through a text but need some help with a compound interest question.

the formula to find compound interest is I = P (1 + R)n–1.

P= principal sum
R= interest rate
n= number of periods for which interest is calculated

John borrows £500 over 2 years from a building society at a rate of 12% per annum compounded
quarterly. How much interest will Shifty have to pay at the end of the 2-year loan?

If £500 is loaned for 2 years at a rate of 12% per annum, compounded quarterly, the
calculations need to be made on a quarterly basis. So the value of n will be 4 (quarters) × 2 (years)
= 8, and the value of r will be 12⁄4 = 3% (per quarter).
According to the question the answer in book is I = 500(1.03)8–1 = £133.38.

Now my issue is when i try to do this with my calculator i get the figure 614.9

I am not sure what I am doing wrong. There are other practice questions, but I want to be sure I am following the correct stages on the calculator before I attempt these. I am using this calculator model View attachment 6280

Any advice would be much appreciated

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You are misunderstanding the formula, "I = P (1 + R)n–1".
To get 614.9 you must have interpreted it as $$I= P(1+ R)^{n-1}$$:
$$500(1+ .03)^7= 500(1.03)^7= 500(1.29)= 614.9$$

But it is $$I= P((1+ R)^n- 1)$$:
$$500((1+ .03)^8- 1)= 500(1.03^8- 1)= 500(1.2667- 1)= 500(0.267)= 133.38$$.

$$P(1+ R)^n$$ is the amount, both initial amount and interest, that must be repaid. The -1, which, after multiplying by P is -P subtracts off the initial amount to leave interest only.

HallsofIvy said:
You are misunderstanding the formula, "I = P (1 + R)n–1".
To get 614.9 you must have interpreted it as $$I= P(1+ R)^{n-1}$$:
$$500(1+ .03)^7= 500(1.03)^7= 500(1.29)= 614.9$$

But it is $$I= P((1+ R)^n- 1)$$:
$$500((1+ .03)^8- 1)= 500(1.03^8- 1)= 500(1.2667- 1)= 500(0.267)= 133.38$$.

$$P(1+ R)^n$$ is the amount, both initial amount and interest, that must be repaid. The -1, which, after multiplying by P is -P subtracts off the initial amount to leave interest only.

Thank you so much HallsofIvy for your prompt reply I suspected it was something to do with my use of brackets. Its just something I need to improve on. Apologies for late response and thanks again.

## Question 1: What is compound interest?

Compound interest is a type of interest that is calculated on both the initial amount of money and any accumulated interest from previous periods. This means that the interest earned in one period is added to the principal amount and then interest is calculated on the new total for the next period.

## Question 2: How is compound interest different from simple interest?

Simple interest is calculated only on the initial principal amount, while compound interest takes into account the accumulated interest as well. This means that compound interest will result in higher earnings over time compared to simple interest.

## Question 3: What factors affect compound interest?

The main factors that affect compound interest are the interest rate, the compounding period, and the initial principal amount. A higher interest rate and more frequent compounding periods will result in higher earnings, while a lower initial principal amount will result in lower earnings.

## Question 4: How can compound interest help me save money?

Compound interest can help you save money by allowing your earnings to grow exponentially over time. As the interest is continuously added to the initial principal amount, the amount of interest earned each period also increases. This can lead to significant earnings over a long period of time.

## Question 5: How can I calculate compound interest?

The formula for calculating compound interest is: A = P(1 + r/n)^(nt), where A is the final amount, P is the principal amount, r is the annual interest rate, n is the number of compounding periods per year, and t is the number of years. However, there are many online calculators and apps available that can do the calculation for you.

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