SOLUTION: 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.

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

RELATED QUESTIONS
At what rate of simplest interest will 1000 accumulate to 1420 in 2.5 years, money double (answered by macston)

ok I have this word problem that I have been struggling on forever, Its in a college math (answered by Alan3354)

a firm will need 300000 at the end of 3 years to repay a loan. the firm decided that it... (answered by math_tutor2020,Theo)

Heather is planning to invest a constant amount of money at the end of every year for 15... (answered by ikleyn)

What amount of money should you invest today, at 6 1/8% simple interest per year, in... (answered by stanbon)

a firm will need 300000 at the end of 3 years to repay a loan. the firm decided that it... (answered by Theo)

Carolyn Ellis is setting up an annuity for her retirement. She can set aside $2000 at... (answered by rfer)

If an amount of P in pesos is invested at r percentage compunded anually to an amount of... (answered by Theo)

City Wide Delivery Service uses vans costing $24800 each. How much will the company have... (answered by Theo)