Answer:
What will Sam have to pay for this equipment if the loan calls for semiannual payments (2 per year)
and monthly payments (12 per year)?
Compare the annual cash outflows of the two payments.
- total semiannual payments per year = $2,820.62 x 2 = $5,641.24
- total monthly payments per year = $531.13 x 12 = $6,373.56
Why does the monthly payment plan have less total cash outflow each year?
- The monthly payment has a higher total cash outflow ($6,373.56 higher than $5,641.24), it is not lower. Since the compounding period is shorter, more interest is charged.
What will Sam have to pay for this equipment if the loan calls for semiannual payments (2 per year)?
- $2,820.62 x 12 payments = $33,847.44 ($25,000 principal and $8,847.44 interests)
Explanation:
cabinet cost $25,000
interest rate 10%
we can use the present value of an annuity formula to determine the monthly payment:
present value = $25,000
PV annuity factor (5%, 12 periods) = 8.86325
payment = PV / annuity factor = $25,000 / 8.8633 = $2,820.62
present value = $25,000
PV annuity factor (0.8333%, 60 periods) = 47.06973
payment = PV / annuity factor = $25,000 / 47.06973 = $531.13