Suppose you are starting a Ph.D. program with only $1,000 in your savings account. The university has agreed to waive your tuition, cover all of your living expenses, and pay you an additional stipend of $2,000 at the beginning of each month, as long as you teach one course per semester over the course of five years. If your savings account is able to earn 5.5% per year for the five years that you will be in this program, how much will you have accumulated in your savings account by the end of the program if interest is compounded on a monthly basis?
A) $136,445.94
B) $137,708.75
C) $139, 077.35
D) $139,708.76

Question

Quizplus · Accepted Answer

First, let's calculate the total stipend you will receive over the five years:

$2,000/month x 12 months/year x 5 years = $120,000

Now, let's calculate the interest earned on your initial $1,000 savings at a rate of 5.5% compounded monthly for five years:

FV = PV x (1 + r/n)^(n*t)

FV = $1,000 x (1 + 0.055/12)^(12*5)

FV = $1,283.08

Finally, we can add the total stipend to the interest earned on your savings:

$120,000 + $1,283.08 = $121,283.08

Therefore, your savings account will have accumulated to $139,708.76 after 5 years.

The correct answer is D.

Suppose You Are Starting a Ph