Answer:
The amount given for the subsequent 17 years assuming the invesmtent yield 9% return is $521.23
Explanation:
We have to solve for the installment of a 17 years annuity discounted at 9% annual considering the first 3 years cash flow and the purchase price:
[tex]\frac{Maturity}{(1 + rate)^{time} } = PV[/tex]
discount rate 0.09
# Cashflow Discounted
0 -5544.87 -5544.87
1 100 91.74
2 500 420.84
3 750 579.14
NPV -4453.15
We solve for the PMT that give that amount:
[tex]PV \div \frac{1-(1+r)^{-time} }{rate} = C\\[/tex]
PV $4,453.1500
time 17
rate 0.09
[tex]4453.15 \div \frac{1-(1+0.09)^{-17} }{0.09} = C\\[/tex]
C $ 521.225
Answer:
The vale of X = $276.11 (to 2 decimal places)
Explanation:
First of all, let us lay out the particulars for clarity.
pay at t 1 = $100
pay at t 2 = $500
pay at t 3 = $750
Amount investment was purchased for = $5,544.87
percentage return on investment = 9% = 0.09.
Next let us calculate amount earned as return on investment from percentage return;
amount earned from percentage;
= 9% of $5544.87 = 0.09 × 5544.87 = $499.0383
Next let us calculate the total expected return on investment after 20 years
= Amount invested + amount earned from percentage
= 5544.87 + 499.0383 = $6043.9083
Therefore, after 20 years, the invested is expected to yield $6043.9083.
Next let us add the total amount gotten after the first 3 years;
t1 + t2 + t3 = 100 + 500 +750 = $1,350
To get the total amount to be earned in the remaining 17 years, we will subtract the amount gotten after the first 3 years from the total amount expected;
= 6043.9083 - 1350 = $4693.9083
Hence in the next 17 years, the amount to be earned is $4693.9083.
X is the fixed cash flow at the end of each year for the remaining 17 years, so to calculate this, we divide the total amount earned in the 17 year period by 17.
∴ X = 4693.9083 ÷ 17 = $276.1123 = $276.11 ( to 2 decimal places)
