Question

How much money should be invested in an account that earns 7% interest compounded quarterly to yield $10,000 in 5 years. (Round to the nearest cent)

Answer 1

In general, the compound interest formula is

`A=P(1+(r)/(n))^(nt)`

In our case, since it is compounded quarterly, n=3 (3 periods of 4 months in a year), and

`n=4,r=7\%=0.07,A=10000,t=5`

Thus, solving for P,

`\begin{gathered} \Rightarrow10000=P(1+(0.07)/(4))^(4\cdot5) \\ \Rightarrow P=(10000)/((1+(0.07)/(4))^(4\cdot5))=(10000)/((1+(0.07)/(4))^(20)) \\ \Rightarrow P\approx7068.25 \end{gathered}`

Thus, the answer is approximately $7068.25

A completely different situation is when we fix

`A=P+10000,r=0.07,n=4`
`\begin{gathered} \Rightarrow P+10000=P(1+(0.07)/(4))^(4\cdot5) \\ \Rightarrow P-P(1+(0.07)/(4))^(4\cdot5)=-10000 \end{gathered}`