Question

the maker of cardboard boxes leases a warehouse and pays $7,000 at the beginning of each month for 5 years. if interest rates are 3.75% compounded monthly, what is the present value (in dollars) of the payments? (round your answer to the nearest cent.) $

Explanation:

Step1: Define given values

Payment per period $PMT = 7000$, annual interest rate $r = 0.0375$, compounding periods per year $n = 12$, time in years $t = 5$, total periods $N = n \times t = 12 \times 5 = 60$, periodic rate $i = \frac{r}{n} = \frac{0.0375}{12} = 0.003125$

Step2: Use annuity due formula

Present Value (PV) of annuity due: $PV = PMT \times \frac{1 - (1 + i)^{-N}}{i} \times (1 + i)$

Step3: Calculate discount factor

First compute $(1 + i)^{-N} = (1 + 0.003125)^{-60} \approx 0.835424$
Then $1 - (1 + i)^{-N} = 1 - 0.835424 = 0.164576$
$\frac{1 - (1 + i)^{-N}}{i} = \frac{0.164576}{0.003125} \approx 52.66432$

Step4: Adjust for annuity due

$PV = 7000 \times 52.66432 \times (1 + 0.003125)$
$PV = 7000 \times 52.66432 \times 1.003125 \approx 7000 \times 52.8285$

Answer:

$369799.50$