Problema Solution
Carmen has $9,000 to invest. She needs $20,000 at the end of 8 years. If the interest is compounded quarterly, find the rate r needed.
Answer provided by our tutors
P = $9,000 is the principal (the money she will invest)
A = $20,000 the future value
t = 8 years
r = ? the annual interest rate
m = 4 is the number of compounding periods per year
n = m*t = 4*8 = 32 is the number of compounding periods
i = r/m = r/4 is the interest rate per period
A = P(1 + i)^n
20,000 = 9,000(1 + r/4)^32
(1 + r/4)^32 = 20,000/9,000
r = 4*((20/9)^(1/32) - 1)
r = 0.101069
or in %
r = 10.1069%
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the rate needed is 10.1069%.