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+(r)/(m))^(mt)`

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

`P=(F)/((1+(r)/(m))^(mt))`

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

`P=(15,000)/((1+(0.044)/(365))^(365*11))`

Then, solve for P.

`P=(15,000)/((1.000120548)^(4015))=(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.