Answer to Question #246975 in Financial Math for Inno

Question

David needs R30 835, 42 to buy a second hand trailer.how lobg will it take him to save towsrds this amount , if he deposit R25 000 now into a savings account earning 10% interest per year compounded weekly

Answer 1

Compound interest

$A=P(1+\dfrac{r}{n})^{nt}$

Solve for $t$

$(1+\dfrac{r}{n})^{nt}=\dfrac{A}{P}$

$nt=\dfrac{\ln(\dfrac{A}{P})}{\ln(1+\dfrac{r}{n})}$

$t=\dfrac{\ln(\dfrac{A}{P})}{n\ln(1+\dfrac{r}{n})}$

Given $A=30 835.42, P=25000, r=0.1, n=52$

$t=\dfrac{\ln(\dfrac{30 835.42}{25000})}{52\ln(1+\dfrac{0.1}{52})}\approx2.0999 (years)$

$t\approx109.2\ weeks$

It will take him 110 weeks to save towards this amount.