Question

Please helppHow much money would you have after 7 years if you invested $12,000 at 2% compounded annually?

Answer 1

Step 1

write the expression for the amount compounded annually or in a given period of time and define the terms

$\begin{gathered} A=P(1+\frac{r}{100})^n \\ \text{where } \\ A=\text{ amount } \\ r\text{ = rate per year = 2\%} \\ n\text{ = time = 7 years} \\ P\text{ = principal = \ 12,000} \end{gathered}$

Step 2

Substitute these values into the above equation and find the amount compounded annually after 7 years

$\begin{gathered} A\text{ = 12000(1+}\frac{2}{100})^7 \\ A\text{ = 12000(1+0.02})^7 \\ A=12000(1.02)^7 \\ A=\text{ 12000}\times1.148685668 \\ A=\text{ \ 13,784.22801} \end{gathered}$

In 7 years, annually, he will compound $13,784.22801

For question 2

Use the formula

$\begin{gathered} A\text{ = P(1+}\frac{0.01r}{n})^{nt} \\ \text{where n = number of times interest is compounded in a year}=\text{ 2, since semi annually which means it is compunded every half of a year and then full of a year anually} \\ t\text{ = time for interest compounded to elapse= 8 years} \\ P\text{ = principal = \ 7,500} \\ A=\text{ Amount} \\ r\text{ = rate = 4.25\%} \\ \end{gathered}$

Substituting these values into the formula yields

$\begin{gathered} A=\text{ 7500(1+}\frac{0.01\times4.25}{2})^{2\times8} \\ A=7500(1.02125)^{16} \\ A=7500\times1.399951895 \\ A=\text{ \ 10.499.3921} \end{gathered}$