Problema Solution
Suppose that you put $2500 into a retirement account that grows with an interest rate of 4.75% compounded once each year. After how many years will the balance of the account be at least $20,000?
Answer provided by our tutors
A => 20,000 the future value after t year
P = $2,500 is the principal
t = the number of years
m = 1 the number of compounding periods per year
n = m*t = t the number of compounding periods
r= 0.0475 or 4.75% the annual interest rate
A = P(1 + r)^n and A>=20,000
P(1 + r)^n >= 20,000
2500(1 + 0.0475)^n >= 20000
by solving we find:
t >= 44.81 years
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after not less than 44.81 years the balance on the account will be at least $20,000.