Question

Suppose you invest $500 in a savings account that pays 3.5% annual interest. When will the account contain at least $650? A. 6 years B. 7 years C. 8 years D. 9 years

Answer 1

Suppose you invest $500

Principal Amount = $500

that pays 3.5% annual interest i.e.

Rate of Interest = 3.5%

Amount = $650

We need to find the time period

The general expression for the compund interest is :

`\text{ Amount = Principal(}1+\frac{rate\text{ of interest}}{100})^(time)`

Substitute the value and simplify :

`\begin{gathered} \text{ Amount = Principal(}1+\frac{rate\text{ of interest}}{100})^(time) \\ 650=500(1+(3.5)/(100))^(time) \\ Divide\text{ both side by 500} \\ (650)/(500)=(500)/(500)(1+(3.5)/(100))^(time) \\ (13)/(10)=(1+(3.5)/(100))^(time) \\ Apply\text{ exponents rule:} \\ Time\text{ ln(1+}(3.5)/(100))=\ln (13)/(10) \\ Time\text{ ln(}(103.5)/(100))=\ln (13)/(10) \\ \text{Time = }\frac{\ln(13)/(10)}{\text{ln(}(103.5)/(100))} \\ \text{Time = }7.6266\text{ years} \\ \text{Time }\approx8years \end{gathered}`

Time = 8 years