Ahmet borrows $700 and is charged compound interest at 15% per year. How much will he have to pay back in total after 6 years? Give your answer to two decimal places.
Question
Ahmet borrows $700 and is charged compound interest at 15% per year. How much will he have to pay back in total after 6 years? Give your answer to two decimal places.
Solution
To calculate the total amount Ahmet will have to pay back after 6 years, we need to use the formula for compound interest, which is:
A = P (1 + r/n) ^ nt
Where: A = the amount of money accumulated after n years, including interest. P = the principal amount (the initial amount of money) r = annual interest rate (in decimal) n = number of times that interest is compounded per year t = time the money is invested for in years
In this case, Ahmet borrows $700, so P = 700. The annual interest rate is 15%, so r = 15/100 = 0.15. The interest is compounded annually, so n = 1. And the time is 6 years, so t = 6.
Substituting these values into the formula, we get:
A = 700 (1 + 0.15/1) ^ (1*6) A = 700 (1 + 0.15) ^ 6 A = 700 * 1.15 ^ 6 A = 700 * 2.47614
So, Ahmet will have to pay back approximately $1732.90 after 6 years.
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