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How much money would need to be deposited into an account earning 5.25% interest compounded annually in order for the accumulated value at the end of 25 years to be $75,000?

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Answer provided by our tutors

P = the principal


t = 25 years the time in years


r = 0.0525 or 5.25% annual rate


m = 1 compounding periods per year


i = 0.0525 or 5.25% interest rate per period


n = t*m = 25 total number of compounding periods


A = $75,000 future value


A = P(1 + i)^n


P(1 + i)^n = A


P(1 + 0.0525)^25 = 75000


by solving we find:


P = $20,869.34
A = P(1+r/n)^(nt)
so
P = A/(1+r/n)^(nt)
P = 75,000/(1 + 0.0525/1)^(1*25)
P = 75,000/(1.0525^25
P = 75,000/3.5937
P = 20,869

answer: You would need $20,869 to be deposited into an account

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