Answer :
In the provided annuity scenarios, calculations were performed to find missing values using the Present Value of Annuity (PVA) formula. Key results include determining the periodic payment for a given present value annuity and solving for time, interest rate, and present value in various situations.
In the given annuity situations, we are tasked with solving for the unknown values using the appropriate factor(s) from the tables provided for Present Value of Annuity (PVA). The formula for PVA is:
[tex]\[ PVA = PMT \times \frac{1 - (1 + i)^{-n}}{i} \][/tex]
Calculating the missing values:
1. For the first situation (n=1, PVA=3000, i=8%), the missing PMT is [tex]\( \frac{3000 \times 0.08}{1 - (1 + 0.08)^{-1}} \)[/tex], resulting in approximately $2429.80.
2. In the second case (n=52, PMT=75000, i=8%), we find the PVA using the formula. The result is approximately $4,500,000.
3. For the third scenario (PMT=20000, i=9%, PVA=161214), we calculate n as [tex]\( \frac{1 - (20000 \times 0.09)}{-161214} \)[/tex], resulting in approximately 4 years.
4. In the fourth case (PMT=500,000, n=4, i=10%), the PVA is [tex]\( \frac{500,000 \times (1 - (1 + 0.10)^{-4})}{0.10} \)[/tex], resulting in approximately $1,805,180.
5. In the fifth situation (n=85, PVA=250,000, i=?), we find i using the formula [tex]\( i = \left(1 - (1 + i)^{-n}\right) \div PVA \)[/tex], resulting in approximately 4.67%.
