Question

You want to buy a house in 5 years and put aside money in a CD for that purpose. The house will cost $425,000 and the CD pays 5%, compounded monthly. How much did you pay for the CD to have that amount in 5 years?

Answer 1

The formula to calculate the money in the CD after t months would be:

$P(1+0.05)^t$

Where P is the principal.

We know that at the end, we will have $425,000 , and that will be after 60 months. Thereby,

$425000=P(1.05)^{60}$

Solving for P,

$\begin{gathered} 425000=P(1.05)^{60} \\ \rightarrow\frac{425000}{(1.05)^{60}}=P \\ \\ \rightarrow22750.60 \end{gathered}$

Thereby, if the interest were compounded monthly, we would need to put $22,750.60 into the CD