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

Answer:

Original sum of money = $2246.51

Step-by-step 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)

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

Hence, the original sum of money borrowed = $2246.51