# Compound interest help

#### logicandtruth

##### New member
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

Any advice would be much appreciated

#### HallsofIvy

##### Well-known member
MHB Math Helper
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.

#### logicandtruth

##### New member
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.