Problema Solution
Suppose $1,000 is compounded quarterly for 4 years. If no other deposits are made, what rate is needed for the balance to double in value.
Answer provided by our tutors
P = $1,000.00 the principal
r = annual rate as a decimal
m = 4 compounding period per year (compounded quarterly)
i = r/4 interest rate per period
t = 4 years number of years
n = m*t = 4*4 = 16 total number of compounding periods
A = 2*P = 2*1000 = $2,000 the future value
A = P(1 + i)^n
2000 = 1000*(1 + r/4)^16
(1 + r/4)^16 = 2000/1000
(1 + r/4)^16 = 2
by solving we find:
r = 0.1771 or 17.71%
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an annual rate of 17.71% is needed.