Answer:
PV = $188,653.22
Explanation:
Given the following information, firstly we need to calculate present value of cash flow for the last 9 years. The present value of cash flow therefore
PVA2= $1,800 {[1 – 1 / (1 + 0.10 / 12)^108] / (0.10 / 12)}
PVA2= $127,852.84
Thus, present value of Cashflow today
PV = $127,852.84 / [1 + (0.08 / 12)]^84+ $1,800{[1 – 1 / (1 + 0.08 / 12)^84] / (0.08 / 12)}
PV = $188,653.22
Answer:
The present value of annuity is $657,720
Explanation:
Present value of an annuity is the total cash value of all future annuity payments, given a determined rate of return or discount rate.
Present value of annuity = P[tex][\frac{1 - (1 + r)^{-n} }{r}][/tex]
where: P is the periodic payment, r is the rate per period and n is the number of periods.
The discount rate is compounded for the first 7 years and thereafter.
The present value of annuity in the first 7 years can be calculated as:
P = $1800 × 12 = $21,600 per year, r = 8% and n = 7 years.
[tex]PV_{7}[/tex] = 21600[tex][\frac{1 - (1 + 0.08)^{-7} }{0.08}][/tex]
= 21600[tex][\frac{0.42}{0.08}][/tex]
[tex]PV_{7}[/tex] = $113,400
Thus, the present value after the first 7 years = $113,400.
Therefore, the present value of the annuity = 113,400[tex][\frac{1 - (1 + 0.1)^{-9} }{0.1}][/tex]
= 113,400[tex][\frac{0.58}{0.1}][/tex]
= $657,720
The present value of annuity is $657,720.
