Problema Solution
Barbara knows that she will need to buy a new car in 3 years. The car will cost $15,000 by then. How much should she invest now at 7%, compounded quarterly, so that she will have enough to buy a new car?
Answer provided by our tutors
P = the principal to be invested
r = 0.07 or 7% annual interest rate
t = 3 years
n = 4*t = 4*3 = 12 compounding periods (the account is compounded quarterly)
A = $15,000 future value
A = P(1 + r/4)^n
P = A/(1 + r/4)^n
P = 15000/(1 + 0.07/4)^12
by solving we find:
P = $12,180.87
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Barbara should invest $12,180.87.