Answer:
(a) The present value is $20,186.75.
(b) The present value is $22,609.16.
(b) The present value is $20,828.46.
Explanation:
(a) The first payment is received at the end of the first year, and interest is compounded annually.
The present value can be determined using the formula for calculating the present value of an ordinary annuity as follows:
PV = P * ((1 - (1 / (1 + r))^n) / r) …………………………………. (1)
Where;
PV = Present value =?
P = Annuity payment = $5,600
r = Annual interest rate = 12%, or 0.12
n = number of years = 5
Substitute the values into equation (1) to have:
PV = $5,600 * ((1 - (1 / (1 + 0.12))^5) / 0.12)
PV = $5,600 * 3.60477620234501
PV = $20,186.75
(b) The first payment is received at the beginning of the first year, and interest is compounded annually.
This can be calculated using the formula for calculating the present value (PV) of annuity due as follows:
PV = P * ((1 - [1 / (1 + r))^n) / r) * (1 + r) .................................. (1)
Where;
Where;
PV = Present value =?
P = Annuity payment = $5,600
r = Annual interest rate = 12%, or 0.12
n = number of years = 5
Substitute the values into equation (1) to have:
PV = $5,600 * ((1 - (1 / (1 + 0.12))^5) / 0.12) * (1 + 0.12)
PV = $5,600 * 3.60477620234501 * 1.12
PV = $22,609.16
(c) The first payment is received at the end of the first year, and interest is compounded quarterly.
The present value can be determined using the formula for calculating the present value of an ordinary annuity as follows:
PV = P * ((1 - (1 / (1 + r))^n) / r) …………………………………. (1)
Where;
PV = Present value =?
P = Quarterly payment = Annuity payment / 4 = $1,400
r = Quarterly interest rate = Annual interest rate / 4 = 12% / 4 = 0.12 / 4 = 0.03
n = number of quarters = 5 years * 4 = 20
Substitute the values into equation (1) to have:
PV = $1,400 * ((1 - (1 / (1 + 0.03))^20) / 0.03)
PV = $1,400 * 14.8774748604555
PV = $20,828.46
