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.