Question

what's the present value of a 4-year ordinary annuity of $2,250 per year plus an additional $1,550 at the end of year 4 if the interest rate is 5%? a.$11,474.44 b.$9,253.58 c.$7,773.01 d.$7,125.25 e.$7,402.86

Answer 1

The present value of a 4-year ordinary annuity can be calculated by finding the present value of each payment and summing them up. In this case, the annuity is $2,250 per year for 4 years, plus an additional $1,550 at the end of year 4. The interest rate is 5%. The present value of the annuity is approximately $9,318.46.

Step-by-step explanation:

The present value of a 4-year ordinary annuity can be calculated by finding the present value of each payment and summing them up. In this case, the annuity is $2,250 per year for 4 years, plus an additional $1,550 at the end of year 4. The interest rate is 5%. To calculate the present value, we can use the formula:

PV = P1 / (1 + r)^1 + P2 / (1 + r)^2 + ... + Pn / (1 + r)^n

where PV is the present value, P1, P2, ..., Pn are the cash flows, r is the interest rate, and n is the number of periods.

Let's calculate the present value:

• P1 = $2,250
• P2 = $2,250
• P3 = $2,250
• P4 = $2,250 + $1,550 = $3,800
• r = 5%
• n = 4

Using the formula, we can calculate the present value as:

PV = $2,250 / (1 + 0.05)^1 + $2,250 / (1 + 0.05)^2 + $2,250 / (1 + 0.05)^3 + $3,800 / (1 + 0.05)^4

Simplifying the calculation, we get the present value as:

PV ≈ $2,143.97 + $2,043.78 + $1,948.84 + $3,181.87

PV ≈ $9,318.46

So, the present value of the annuity is approximately $9,318.46.

Answer 2

To find the present value of the annuity, calculate the present value of each payment and sum them up. The present value of the $2,250 payments are $2,142.86, $2,041.40, $1,945.14, and $1,853.66. The present value of the additional $1,550 payment at the end of year 4 is $1,245.98. The total present value is $9,229.04.

Step-by-step explanation:

To find the present value of a 4-year ordinary annuity, you need to calculate the present value of each individual payment and then sum them up. Let's start by finding the present value of the $2,250 payments. Using the present value formula, we have:

1. $2,250 / (1 + 0.05)1 = $2,142.86
2. $2,250 / (1 + 0.05)2 = $2,041.40
3. $2,250 / (1 + 0.05)3 = $1,945.14
4. $2,250 / (1 + 0.05)4 = $1,853.66

Now, let's find the present value of the additional $1,550 payment at the end of year 4:

$1,550 / (1 + 0.05)4 = $1,245.98

Finally, sum up all the present values to find the total present value:

$2,142.86 + $2,041.40 + $1,945.14 + $1,853.66 + $1,245.98 = $9,229.04

Therefore, the present value of the annuity is $9,229.04, which is option b.$9,253.58.