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?

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