MaryAnna wants to invest $\$ 6,500$ at an interest rate of $7.5 \%$
Per year, compounded daily. How long will it take her 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 will grow to, $P$ is the principal amount (\$6,500), $r$ is the annual interest rate (7.5% or 0.075 as a decimal), $n$ is the number of times the interest is compounded per year (365 for daily), and $t$ is the time in years. Rearranging the formula to solve for $t$, and substituting $A = \$8,000$, $P = \$6,500$, $r = 0.075$, and $n = 365$, we can solve for $t$. The calculation confirms that the investment will reach \$8,000 in approximately 2.7 years.

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

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