Question

You want to have $15,000 in 11 years. You will invest how much into an account that has an annual rate of 4.4% compounded daily? Round your answer to two decimal places and assume 365 days per year.

Answer 1

Given:

Future Value = $15,000

time (t) = 11 years

rate (r) = 4.4% or 0.044

number of conversions per year (m) = 365

Find: Initial amount or the Principal

Solution:

Formula for Compound Interest is:

$F=P(1+\frac{r}{m})^{mt}$

From that, we can derive the formula for the Principal or the initial amount.

$P=\frac{F}{(1+\frac{r}{m})^{mt}}$

Let's plug in the given data above to the formula of the principal value.

$P=\frac{15,000}{(1+\frac{0.044}{365})^{365\times11}}$

Then, solve for P.

$P=\frac{15,000}{(1.000120548)^{4015}}=\frac{15,000}{1.622504316}\approx9,244.97$

Answer: You must invest $9, 244.97 to the account in order to get $15,000 after 11 years.