Question

Suppose you are starting a PhD 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

Answer 1

Answer:

savings balance at the end of 5 years: 139.708,75‬

Explanation:

We have to solve for the 1,000 dollar and the annuity given by the college future value:

$C \times \frac{(1+r)^{time} -1}{rate} (1+r)= FV$

C 2,000.00

time 60 (5 years x 12)

rate 0.004583333  (0.055 annual  / 12 months)

$2000 \times \frac{1-(1+0.004583)^{-60} }{0.004583} (1+0.004583)= FV$

FV $138,393.0537

$Principal \: (1+ r)^{time} = Amount$

Principal 1,000.00

time 60.00

rate 0.00458

$1000 \: (1+ 0.00458333333333333)^{60} = Amount$

Amount 1,315.70

Total 139.708,75‬