Question

Mr Chua borrows a sum of money from the bank which charges a compound interest of 4.2% per annum, compounded 6.Given that Mr Chua had to pay 96.60% in the interest payments at the end of the first year, find the original sum of money borrowed, giving your answer correct to the nearest cent

Answer 1

Original sum of money = $2246.51

Explanation:

Interest = $96.60

Interest is compounded 6 times in a year ; n = 6

time = 1 year ; Rate of interest (r) = 4.2%

Interest = Future Value - Principal Value ...........(1)

`\text{Future Value = }Principal\cdot (1+(r)/(100* n))^(n\cdot t)\\\\\text{Substituting this value in equation (1) , We get }\\\\Interest=Principal\cdot (1+(r)/(100* n))^(n\cdot t)-Principal\\\\\implies 96.60=Principal[\cdot (1+(4.2)/(100* 6))^(6\cdot 1)-1]\\\\\implies Principal=\$2246.51`

Hence, the original sum of money borrowed = $2246.51