Question

Given a 7 percent interest rate, compute the present value of payments made in years 1, 2, 3, and 4 of $1,350, $1,550, $1,550, and $1,850, respectively. (Do not round intermediate calculations and round your final answer to 2 decimal places.) Present value

Answer 1

Present value formula:

PV Σ P (1 + 1)"

Where,
PV = Present value of payments
P = Payments of each year
i = interest rate in decimal form
n = number of years

Therefore,

$\textup{PV} = \frac{1350}{(1+0.07)^1} + \frac{1550}{(1+0.07)^2} + \frac{1550}{(1+0.07)^3} + \frac{1850}{(1+0.07)^4}$

$= \frac{1350}{1.07} + \frac{1550}{1.1449} + \frac{1550}{1.22504} + \frac{1850}{1.310796}$

$= \textup{1,261.68 + 1,353.83 + 1,265.26 + 1,411.36 }$

$= \textup{\$\,5,292.13 }$

Therefore, the present value of the payments is $5,292.13