If Porthos wants $25,000 after 8 years to make a down payment on a home, how much does he need to invest every quarter, into an account that pays 2% compounded quarterly?
What is the simplified denominator?
32 quarters at 0.5 percent or 0.005 and 32 deposits of amount P
25,000 = P [ (1.005)^32 -1 ] / 0.005
numerator: m(1.173)-1
denominator: 0.005
answer: $107.42
hope this helps.
To find out how much Porthos needs to invest every quarter, we can use the future value formula of compound interest:
Future Value = Present Value * (1 + interest rate / number of compounding periods)^(number of compounding periods * number of years)
Given:
- Porthos wants $25,000 after 8 years.
- The interest rate is 2%, compounded quarterly.
Let's denote the amount Porthos needs to invest every quarter as X.
The future value of Porthos' investment after 8 years can be calculated using the formula:
$25,000 = X * (1 + 0.02 / 4)^(4 * 8)
Simplifying the formula:
$25,000 = X * (1 + 0.005)^(32)
$25,000 = X * (1.005)^(32)
To isolate X, we divide both sides of the equation by (1.005)^32:
$25,000 / (1.005)^32 = X
Now we can compute the value of X to find out how much Porthos needs to invest every quarter.
25000 = 235 P
P = about $106