Question

Pamela borrows an amount of money for emergency house repairs. The interest on the loan is compounded

quarterly. After four years the debt accumulated by R7 980,00 to the amount of R32 923,00. The yearly

interest rate, expressed as a percentage and rounded to two decimal places, at which the money was borrowed,

is

Answer 1

According to the compound interest formula

$R=P*(1+{\frac i n})^{t*n}\implies i =n*(({\frac R P})^{{\frac 1 {tn}}}-1)$ , where P - initial amount, i - yearly interest rate, n - number of payments per year, t - number of years

So, in the given case we have

$i=4(({\frac {32923} {7980}})^{{\frac 1 {4*4}}}-1)=0.37$ = 37% yearly