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

AI Thread Summary
The discussion centers on calculating compound interest using the formula I = P((1 + R)^n - 1). A user is confused about their calculator results for a loan of £500 at a 12% annual interest rate compounded quarterly over two years. They mistakenly calculated the interest using the wrong interpretation of the formula, leading to an incorrect figure of £614.9 instead of the correct £133.38. Clarification was provided on the importance of correctly applying the formula and using brackets appropriately. The user expressed gratitude for the guidance and acknowledged the need to improve their understanding of the calculations.
logicandtruth
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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.
 
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