Question

1. Solve:

a. What is the present value of a regular $1,000 60-month annuity, if r is 6% APR compounded monthly?

b. What is the present value of a $1,000 60-month annuity due, if r is 6% APR compounded monthly?

c. What is the present value of a $1,000 60-month annuity, starting 6 months from today, if r is 6% APR compounded monthly?

Answer 1

Answer a.

Monthly Payment = $1,000
Number of Payments = 60

Annual Interest Rate = 6.00%
Monthly Interest Rate = 6.00% / 12
Monthly Interest Rate = 0.50%

Present Value = $1,000/1.005 + $1,000/1.005^2 + … + $1,000/1.005^59 + $1,000/1.005^60
Present Value = $1,000 * (1 - (1/1.005)^60) / 0.005
Present Value = $1,000 * 51.72556
Present Value = $51,725.56

Answer b.

Monthly Payment = $1,000
Number of Payments = 60

Annual Interest Rate = 6.00%
Monthly Interest Rate = 6.00% / 12
Monthly Interest Rate = 0.50%

Present Value = $1,000 + $1,000/1.005 + … + $1,000/1.005^58 + $1,000/1.005^59
Present Value = $1,000 * 1.005 * (1 - (1/1.005)^60) / 0.005
Present Value = $1,000 * 51.98419
Present Value = $51,984.19

Answer c.

Monthly Payment = $1,000
Number of Payments = 60

Annual Interest Rate = 6.00%
Monthly Interest Rate = 6.00% / 12
Monthly Interest Rate = 0.50%

Present Value = $1,000/1.005^6 + $1,000/1.005^7 + … + $1,000/1.005^64 + $1,000/1.005^65
Present Value = $1,000 * (1/1.005)^5 * (1 - (1/1.005)^60) / 0.005
Present Value = $1,000 * 50.45159
Present Value = $50,451.59