Question

Mariah is putting $5,270 into an account earning 3.75% interest compounded quarterly. She estimates that it will take just over 9 years for this investment to grow to $8,000. Which of the following is a true statement?
a.
Mariah’s estimate of the time is too low.
b.
Mariah’s estimate of the time is correct.
c.
Mariah’s estimate of the time is too high.
d.
Mariah does not have enough information to estimate the time.




Please select the best answer from the choices provided

Answer 1

Answer:

a. Mariah’s estimate of the time is too low

Step-by-step explanation:

To answer this question, we are going to need to input the values in the question into the compound interest formula:

$A=P(1+\frac{r}{n} )^{nt}$

P = initial balance

r = interest rate (decimal)

n = number of times compounded annually

t = time

First, change 3.75% into a decimal:

3.75% -> $\frac{3.75}{100}$ -> 0.0375

Since the interest is compounded quarterly, we will use 4 for n. Lets plug in the values now:

$A=5,270(1+\frac{0.0375}{4})^{4(9)}$

$A=7,373.98$

Mariah's estimate of the time is too low. Your answer is A.