Suppose you borrowed a certain amount of money 509 weeks ago at an annual interest rate of 2.6% with semi annual compounding (2 times per year). If you returned $14687 today, how much did you borrow?

Ivan Buckley

Ivan Buckley

Answered question

2022-09-18

Suppose you borrowed a certain amount of money 509 weeks ago at an annual interest rate of 2.6% with semi annual compounding (2 times per year). If you returned $14687 today, how much did you borrow?

Answer & Explanation

Triston Donaldson

Triston Donaldson

Beginner2022-09-19Added 10 answers

Compound interest formula is
A = P ( 1 + r n ) n t
For semi-annual compounding,
r = 2.6 % = 0.026 , n = 2 , t = 509 52 = 9.7885 , A = 14687
Substitute in the above =n to calculate P
14687 = A ( 1 + 0.026 2 ) 2 ( 9.7885 )
This implies,
A = 14687 ( 1.013 ) 19.577 => A = 11405.56971 A = $ 11405.57
Hence, money borroed 509 weeks ago is $11405.57

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