The future value of an investment is the worth of the investment in a given time.
Ed's monthly payment to meet up with Steve's is $4701.
We have:
Steve
[tex]n=46[/tex] --- time
[tex]r = 8\%[/tex] --- rate
[tex]PMT = 3200[/tex] --- monthly payments
First, we calculate the Steve's future value
[tex]FV = \frac{PMT \times ((1 + r)^{n - 1}) \div r}{1 + r}[/tex]
So, we have:
[tex]FV = \frac{3200 \times ((1 + 8\%)^{46 - 1}) \div 8\%}{1 + 8\%}[/tex]
[tex]FV = \frac{3200 \times ((1 + 0.08)^{45}) \div 0.08}{1 + 0.08}[/tex]
[tex]FV = \frac{3200 \times (1.08)^{45} \div 0.08}{1.08}[/tex]
[tex]FV = 1182238.87[/tex]
For Ed, we have, the following parameters
[tex]n=41[/tex] --- time
[tex]r = 8\%[/tex] --- rate
[tex]FV = 1182238.87[/tex] ---- Ed's future value is the same as Steve's
So, we have:
[tex]FV = \frac{PMT \times ((1 + r)^{n - 1}) \div r}{1 + r}[/tex]
[tex]1182238.87 = \frac{PMT \times ((1 + 0.08)^{41 - 1}) \div 0.08}{1 + 0.08}[/tex]
[tex]1182238.87 = \frac{PMT \times ((1 + 0.08)^{41 - 1}) \div 0.08}{1.08}[/tex]
Multiply by 1.08 x 0.08
[tex]0.08 \times 1.08 \times 1182238.87 = PMT \times ((1 + 0.08)^{41 - 1})[/tex]
[tex]102145.44 = PMT \times ((1.08)^{40})[/tex]
Make PMT the subject
[tex]PMT = \frac{102145.44}{(1.08)^{40}}[/tex]
[tex]PMT = 4701[/tex] --- approximated
Hence, Ed's monthly payment to meet up with Steve's is $4701.
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