Brian wants to invest $\$ 6,500$ at an interest rate of $7.5 \%$ Per year, compounded daily. How long will it take his investment to grow to $\$ 8,000 ?$
A) $2.7 \text { years }$
B) $27 \text { years }$
C) $0.27 \text { years }$
D) $37 \text { years }$
E) $1 \text { year }$

Question

Quizplus · Accepted Answer

To find the time it takes for an investment to grow to a certain amount with daily compounding interest, we use the formula $A = P(1 + \frac{r}{n})^{nt}$, where $A$ is the amount the investment grows to, $P$ is the principal amount, $r$ is the annual interest rate, $n$ is the number of times the interest is compounded per year, and $t$ is the time in years. Plugging in the given values: $8000 = 6500(1 + \frac{0.075}{365})^{365t}$. Solving for $t$ gives approximately $2.7$ years.

Brian Wants to Invest $6,500\$ 6,500$6,500 At an Interest Rate Of 7.5%7.5 \%7.5%

Brian Wants to Invest $\$ 6,500$ At an Interest Rate Of $7.5 \%$