Question

Hsu-Mei wants to save $6,000 for a down payment on a car. To the nearest dollar, how much will she need to invest in an account now with 7.4% APR, compounded daily, in order to reach her goal in 3 years?

Answer 1

Suppose the invested amount is P;

Given that;

`\begin{gathered} r=7.4\text{ \%}=0.074 \\ \\ rate\text{ }per\text{ }day=(0.074)/(365) \end{gathered}`

Also;

`\begin{gathered} t=3years=3*365day \\ \\ t=1095days; \\ \\ A=6000 \end{gathered}`

Thus;

`\begin{gathered} 6000=P(1+(0.074)/(365))^(1095) \\ \\ P=4805.60 \end{gathered}`