Question

a 20-year annuity pays $1,500 monthly, and payments are made at the end of each month. if the interest rate is 6.25 percent compounded monthly for the first ten years and 5.50 percent compounded monthly after that, what is the pv of the annuity?

Answer 1

To find the present value (PV) of the annuity, we need to calculate the present value of each individual payment and then sum them up. The annuity pays $1,500 monthly for 20 years and uses different interest rates for the first 10 years and the remaining 10 years.

Step-by-step explanation:

To find the present value (PV) of the annuity, we need to calculate the present value of each individual payment and then sum them up. The annuity pays $1,500 monthly for 20 years. We will use different interest rates for the first 10 years (6.25%) and the remaining 10 years (5.50%)

For the first 10 years, we can use the formula for present value of an annuity:

PV = R * [(1 - (1 + i)^(-n)) / i]

where R is the monthly payment, i is the interest rate per month, and n is the number of months. Plugging in the values, we ge

PV = 1500 * [(1 - (1 + 0.0625/12)^(-10*12)) / (0.0625/12)]

For the remaining 10 years, we can use the same formula with the new interest rate:

PV = 1500 * [(1 - (1 + 0.055/12)^(-10*12)) / (0.055/12)]

Adding the two present values together, we get the final PV of the annuity.