Question

A person invested $7, 900 in an account growing at a rate allowing the money todouble every 8 years. How much money would be in the account after 5 years, to thenearest dollar?

Answer 1

Given,

The principal amount is $7900.

The time period is 8 years.

The amount of the investment is double of the principal.

Required:

The money would be in the account after 5 years, to the nearest dollar.

The Amount is calculated as:

$\begin{gathered} Amount\text{ = }\frac{Principal\times rate\times time}{100}+principal \\ Amount=(\frac{\text{rate}\times\text{t}\imaginaryI\text{me}}{\text{100}}\text{+1\rparen pr}\imaginaryI\text{nc}\imaginaryI\text{pal} \end{gathered}$

Substituting the value in the above formula then,

$\begin{gathered} 15800=(\frac{\text{rate}\times8}{\text{100}}\text{+1\rparen7900} \\ 2=\frac{rate\times8}{100}+1 \\ 1=rate\times\frac{8}{100} \\ rate=\frac{100}{8} \\ Rate=12.5\text{ \%} \end{gathered}$

The amount in the account after 5 years is:

$\begin{gathered} Amount\text{ =7900\lparen}\frac{5\times12.5}{100}+1) \\ =7900\times\frac{162.5}{100} \\ =12837.5 \end{gathered}$

Hence, money would be in the account after 5 years is $12837.5