Question

Find the present value of the ordinary annuity. Payments of $65,000 made semiannually for 12 years at 4.2% compounded semiannually

A) $2,001, 729.49
B) $1, 096, 114.50
C) $1, 205, 126.00
D) $1, 220, 921.00

Answer 1

The present value of the ordinary annuity is $283,595.95.

Step-by-step explanation:

The present value of the ordinary annuity can be calculated using the formula:

PV = PMT * ((1 - (1 + r/n)^(-nt)) / (r/n)), where PV is the present value, PMT is the periodic payment, r is the interest rate, n is the number of compounding periods per year, and t is the number of years.

In this case, the periodic payment is $65,000, the interest rate is 4.2%, and the compounding frequency is semiannually. The number of years is 12.

1. First, we need to calculate the number of compounding periods. Since the compounding is semiannually, the number of compounding periods would be 2 times the number of years, which is 24.
2. Next, we can plug the values into the formula: PV = $65,000 * ((1 - (1 + 0.042/2)^(-24*12)) / (0.042/2)).
3. Simplifying this equation, we get PV = $65,000 * ((1 - (1.021)^(288)) / (0.021)).
4. Calculating further, PV = $65,000 * ((1 - 1.908366) / 0.021).
5. Finally, PV = $65,000 * (0.091634 / 0.021) = $65,000 * 4.36303 = $283,595.95.