Answer:
To find the present value of the future payments, you can use the formula for the present value of a series of future cash flows, which is given by:
\[ PV = \frac{CF_1}{(1 + r)^t_1} + \frac{CF_2}{(1 + r)^t_2} + \frac{CF_3}{(1 + r)^t_3} \]
Where:
- \(PV\) is the present value,
- \(CF_1, CF_2, CF_3\) are the cash flows (future payments),
- \(r\) is the interest rate per compounding period, and
- \(t_1, t_2, t_3\) are the time periods.
In your case:
- \(CF_1 = 4510\), \(t_1 = 7\),
- \(CF_2 = 3780\), \(t_2 = 13\),
- \(CF_3 = 5125\), \(t_3 = 21\),
- \(r = 0.0864/12\) (monthly interest rate).
Calculate this to find the present value of the future payments. Then, to find the single amount three months from now, you can use the future value formula:
\[ FV = PV \times (1 + r)^t \]
Where:
- \(FV\) is the future value (single amount),
- \(PV\) is the present value calculated earlier,
- \(r\) is the monthly interest rate, and
- \(t = 3\) (time in months).
Calculate \(FV\) to find the single amount three months from now that will pay off the entire loan.