Answer:
[tex]\large\boxed{\large\boxed{\$ 290,281.60}}[/tex]
Explanation:
You have to calculate the present value of $8,700-monthly payments, over 3 years, with a discount rate of 5%, compounded monthly.
This is, the present value of a constant amount at a fixed rate.
There is a special formula to calculate that; it is called present value of an annuity:
[tex]\text{PV of an Annuity} = C\times {[\frac{1}{r}-\frac{1}{r(1+r)^t}]}[/tex]
In this case, it is not an annuity but the monthly payments.
In that formula:
Substituting:
[tex]PV = \$ 8,700\times {[\frac{1}{(0.05/12)}-\frac{1}{(0.05/12)(1+(1+0.05/12)^{36}}]}[/tex]
Computing:
[tex]PV=\$ 290,281.60[/tex]
Explanation:
You have to calculate the present value of $8,700-monthly payments, over 3 years, with a discount rate of 5%, compounded monthly.
This is, the present value of a constant amount at a fixed rate.
There is a special formula to calculate that; it is called present value of an annuity:
\text{PV of an Annuity} = C\times {[\frac{1}{r}-\frac{1}{r(1+r)^t}]}PV of an Annuity=C×[
r
1
−
r(1+r)
t
1
]
In this case, it is not an annuity but the monthly payments.
In that formula:
PV = present value
C = constant payment = $8,700
r = 5% / 12 = 0.05/12
t = 3 × 12 = 36 months
Substituting:
PV = \$ 8,700\times {[\frac{1}{(0.05/12)}-\frac{1}{(0.05/12)(1+(1+0.05/12)^{36}}]}PV=$8,700×[
(0.05/12)
1
−
(0.05/12)(1+(1+0.05/12)
36
1
]
Computing:
PV=\$ 290,281.60PV=$290,281.60
