SOLUTION: Tuition of $1044 will be due when the spring term begins in 7 months. What amount should a student deposit today, at 7.62% to have enough to pay the tuition?

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Question 1020819: Tuition of $1044 will be due when the spring term begins in 7 months. What amount should a student deposit today, at 7.62% to have enough to pay the tuition?
Answer by mathmate(429) About Me  (Show Source):
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Quesion:Tuition of $1044 will be due when the spring term begins in 7 months. What amount should a student deposit today, at 7.62% to have enough to pay the tuition?

Solution:
We'll need the compound interest formula.
It is not mentioned the compounding period in the question. However, many of the bank accounts today offer monthly compounding, and this will be used as the basis.

i=interest rate=7.62% p.a => 7.62/12=0.635% per month
FV=PV(1+i)^n
FV=future value = 1044
PV=present value, to be found
i=interest rate per compounding period (month)=0.00635
n=number of periods=7
1044=PV(1+0.00635)^7
PV=1044/(1.00635^7)=$998.751

In case interest is not compounded, we could apply the simple interest formula:
FV=PV(1+ni)
PV=1044/(1+7*0.00635)
=$999.569