Answer:
The value of this deferred annuity today on his 50th birthday is <u>$2,621.27</u>.
Explanation:
Since the student's desired return of 6% will also start to be paid starting on his 65th birthday, the value of this deferred annuity today on his 50th birthday can be calculated by first calculating the value of the investment on the 65th birthday.
We therefore proceed with the following two steps:
Step 1: Calculation of the value of the investment on the 65th birthday
The value of the investment on the 65th birthday can be calculated 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 at 65 = Present value of the annuity at 65th birthday =?
P = Annuity payment = Invested amount * Student's desired return = $8,900 * 6% = $534
r = Student's desired return rate = 6%, or 0.06
n = number of more years anticipate to live after 65th birthday = 21
Substitute the values into equation (1) to have:
PV at 65 = $534 * ((1 - (1 / (1 + 0.06))^21) / 0.06)
PV at 65 = $534 * 11.764076621288
PV at 65 = $6,282.02
Therefore, the value of the investment on the 65th birthday is $6,282.02.
Step 2: Calculation of the value of this deferred annuity today on his 50th birthday
The value of this deferred annuity today on his 50th birthday can therefore be calculated using the simple present value for as follows:
PV at 50 = PV at 65 / (1 + r)^N …………………………….. (2)
Where;
PV at 50 = the value of this deferred annuity today on his 50th birthday = ?
PV at 65 = Present value of the annuity at 65th birthday = $6,282.02
r = Student's desired return rate = 6%, or 0.06
N = number of years from 50th birthday to 65th birthday = 65 - 50 = 15
Substitute the values into equation (2) to have:
PV at 50 = $6,282.02 / (1 + 0.06)^15
PV at 50 = $6,282.02 / 2.39655819309969
PV at 50 = $2,621.27
Therefore, the value of this deferred annuity today on his 50th birthday is <u>$2,621.27</u>.
