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?

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

b

step-by-step explanation:

take the logarithm of both sides (the base of the log doesn't matter):

apply the exponent property - this says that :

distribute the log terms on both sides:

group like terms together:

divide through both sides by the coefficient on :

you can do some additional rewriting here using the properties of the logarithm to simplify things if you like: