Annuity due

Definition

An annuity due is a series of equal payments made at the beginning of each period over a specified number of periods. This payment structure affects the time value of money since the payments are received sooner than in an ordinary annuity, resulting in a higher present value for the same payment amount and interest rate.

5 Must Know Facts For Your Next Test

1. The formula for calculating the present value of an annuity due is PV = Pmt × [(1 - (1 + r)^{-n}) / r] × (1 + r), where Pmt is the payment amount, r is the interest rate per period, and n is the total number of payments.
2. Annuities due are often used in real estate leases and insurance contracts where payments are required upfront.
3. Due to receiving payments earlier, an annuity due has a higher present value compared to an ordinary annuity with the same payment amount and interest rate.
4. The first payment in an annuity due occurs immediately, which means it has not yet accrued interest, impacting the overall calculation.
5. Understanding annuities due is essential for financial planning and retirement savings, as it affects how much you need to save and when you receive your funds.

Review Questions

• How does the timing of payments in an annuity due affect its present value compared to an ordinary annuity?
  • In an annuity due, payments are made at the beginning of each period, which means they are received sooner than in an ordinary annuity where payments are made at the end. This earlier receipt increases the present value because each payment has more time to accrue interest. Consequently, for the same payment amount and interest rate, an annuity due will always have a higher present value compared to an ordinary annuity.
• Calculate the present value of an annuity due that pays $1,000 annually for 5 years at an interest rate of 5%. What does this calculation reveal about the impact of timing on cash flows?
  • Using the formula for present value of an annuity due, PV = Pmt × [(1 - (1 + r)^{-n}) / r] × (1 + r), we plug in Pmt = $1,000, r = 0.05, and n = 5. This gives us PV = $1,000 × [(1 - (1 + 0.05)^{-5}) / 0.05] × (1 + 0.05) = $4,329.48. This result highlights how receiving cash flows sooner increases their present value significantly compared to an ordinary annuity.
• Evaluate how understanding annuities due can influence personal financial planning strategies for retirement savings.
  • Understanding annuities due allows individuals to plan their retirement savings more effectively by considering how payment timing impacts their future cash flows. If one opts for retirement products that function as annuities due, they could enhance their cash flow position early in retirement. This strategic choice can lead to better investment opportunities as funds become available sooner, allowing for compounded growth over time and facilitating more robust financial security during retirement.

Related terms

ordinary annuity: An ordinary annuity involves equal payments made at the end of each period, contrasting with an annuity due where payments are made at the beginning.

present value: Present value is the current worth of a future sum of money or stream of cash flows given a specified rate of return.

future value: Future value refers to the amount of money that an investment will grow to over a period at a given interest rate.