Answer:
Answer for the question:
For each of the following annuities, calculate the present value. (Enter rounded answers as directed, but do not use rounded numbers in intermediate calculations. Round your answers to 2 decimal places (e.g., 32.16).) Present Value Annuity Payment Interest Rate Years $ _____ $ 2,100 8 % 7 $ _____ $ 1,095 7 % 9 $ $11,000 9 % 18 $ $ 30,000 11 % 28
is given in the attachment.
Explanation:
Answer:
1. $10,933.38
2. $7,134.18
3. $96,311.88
4. $258,048.65
Explanation:
To calculate this, we employ the formula for calculating the present value of an ordinary annuity assuming their payments are made at end of each year. The formula is as follows:
PV = P × [{1 - [1 ÷ (1+r)]^n} ÷ r] …………………………………. (1)
Where;
PV = Present value
P = Annuity payment
r = interest rate
n = number of years
We now proceed as follows:
1. Calculation of PV of $2,100 annuity payment
PV = ?
P = $2,100
r = 8% = 0.08
n = 7
Substitute the values into equation (1) to have:
PV = 2,100 × [{1 - [1 ÷ (1+0.08)]^7} ÷ 0.08]
= 2,100 × [{1 - [1 ÷ 1.08]^7} ÷ 0.08]
= 2,100 × [{1 - [0.925925925925926]^7} ÷ 0.08]
= 2,100 × [{1 - 0.583490395262134} ÷ 0.08]
= 2,100 × [0.416509604737866 ÷ 0.08]
= 2,100 × 5.20637005922332
PV = $10,933.38
Therefore, the PV of $2,100 annuity payment at interest rate of 8% for 7 years is $10,933.38.
2. Calculation of PV of $1,095 annuity payment
PV = ?
P = $1,095
r = 7% = 0.07
n = 9
Substitute the values into equation (1) to have:
PV = 1,095 × [{1 - [1 ÷ (1+0.07)]^9} ÷ 0.07]
= 1,095 × [{1 - [1 ÷ 1.07]^9} ÷ 0.07]
= 1,095 × [{1 - [0.934579439252336]^9} ÷ 0.07]
= 1,095 × [{1 - 0.543933742584148} ÷ 0.07]
= 1,095 × [0.456066257415852 ÷ 0.07]
= 1,095 × 6.51523224879788
PV = $7,134.18
Therefore, the PV of $1,095 annuity payment at interest rate of 7% for 9 years is $7,134.18.
3. Calculation of PV of $11,000 annuity payment
PV = ?
P = $11,000
r = 9% = 0.09
n = 18
Substitute the values into equation (1) to have:
PV = 11,000 × [{1 - [1 ÷ (1+0.09)]^18} ÷ 0.09]
= 11,000 × [{1 - [1 ÷ 1.09]^18} ÷ 0.09]
= 11,000 × [{1 - [0.917431192660550]^18} ÷ 0.09]
= 11,000 × [{1 - 0.211993740150311} ÷ 0.09]
= 11,000 × [0.788006259849689 ÷ 0.09]
= 11,000 × 8.75562510944098
PV = $96,311.88
Therefore, the PV of $11,000 annuity payment at interest rate of 9% for 18 years is $96,311.88.
4. Calculation of PV of $30,000 annuity payment
PV = ?
P = $30,000
r = 11% = 0.11
n = 28
Substitute the values into equation (1) to have:
PV = 30,000 × [{1 - [1 ÷ (1+0.11)]^28} ÷ 0.11]
= 30,000 × [{1 - [1 ÷ 1.11]^28} ÷ 0.11]
= 30,000 × [{1 - [0.900900900900901]^28} ÷ 0.11]
= 30,000 × [{1 - 0.053821598725563} ÷ 0.11]
= 30,000 × [0.946178401274437 ÷ 0.11]
= 30,000 × 8.60162182976761
PV = $258,048.65
Therefore, the PV of $30,000 annuity payment at interest rate of 11% for 28 years is $258,048.65.
