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 numerator?
m(431439)-1
m(1.173)-1
m(1.614)-1
m(435655)-1
Can't figure out what those choices are , none of them make sense
i = .02/4 = .005
n = 4(8) = 32
Amount = 25000
payment ---- p
p( 1.005^32 - 1)/.005 = 25000
p(1.17304. - 1) = 125
p = $106.56
I see m(1.173)-1 , but the brackets would be in the wrong place
Thank you, how would i solve for the bottom portion?
numerator: m(1.173)-1
denominator: 0.005
answer: $107.42
hope this helps.
To calculate how much Porthos needs to invest every quarter, we can use the formula for compound interest:
Future Value = Present Value * (1 + interest rate / number of compounding periods) ^ (number of compounding periods * number of years)
In this case, Porthos wants to have $25,000 after 8 years, and the account pays 2% interest compounded quarterly.
First, we can rearrange the formula:
Present Value = Future Value / (1 + interest rate / number of compounding periods) ^ (number of compounding periods * number of years)
Now we can plug in the values:
Present Value = $25,000 / (1 + 0.02 / 4) ^ (4 * 8)
Simplifying the expression:
Present Value = $25,000 / (1.005) ^ (32)
Now, we can calculate the numerator:
m(431439) - 1 = (4 * 31 * 14 * 3 * 9) - 1 = 431439
Therefore, the simplified numerator is m(431439) - 1.