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Question 1198536: What sum of money would Max need to invest to accumulate a total of $100000 at the end of 7 years at 8% p.a. interest compounding biannually? Answer to the nearest cent.
Answer by math_tutor2020(3817)   (Show Source):
You can put this solution on YOUR website!
Compounding interest formula
A = P*(1+r/n)^(n*t)
A = final amount after t years
P = deposit, aka starting amount
r = annual interest rate in decimal form
n = compounding frequency
t = number of years
biannual = once every six months (aka twice a year)
So we have n = 2
The goal is to have A = 100000 dollars at the end of t = 7 years, where the money is compounded n = 2 times a year.
The interest rate in decimal form is r = 0.08
Your teacher asks you to find the deposit P.
Summary of values
A = 100000
P = unknown
r = 0.08
n = 2
t = 7
Let's solve for P.
A = P*(1+r/n)^(n*t)
100000 = P*(1+0.08/2)^(2*7)
100000 = P*(1+0.04)^(14)
100000 = P*(1.04)^(14)
100000 = P*1.7316764476028
100000 = 1.7316764476028P
1.7316764476028P = 100000
P = 100000/1.7316764476028
P = 57747.5082821806
P = 57747.51
Answer: Max needs to invest $57,747.51
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