Answer:
I must deposit $297.59 each month
Explanation:
Future Value
A series of deposits of R dollars each for n periods at an interest rate i will generate a final value M, given by
[tex]M=F_m\cdot R[/tex]
Where Fm is computed by
[tex]\displaystyle F_m=\frac{(1+i)^n-1}{i}[/tex]
The question provides us with the values
i=10.15% , n=40 years
Converting to monthly periods
[tex]\displaystyle i=\frac{10.15}{100\cdot 12}=0.00846[/tex]
[tex]n=40\cdot 12=480[/tex]
Therefore
[tex]\displaystyle F_m=\frac{(1+0.00846)^{480}-1}{0.00846}=6,619.84[/tex]
Solving the first equation for R
[tex]\displaystyle R=\frac{FV}{F_m}=\frac{1,970,000}{6,619.84}=297.59[/tex]
R=$297.59
