High School
SAT
ACT
University
MCAT
LSAT
DAT
Wize University Introduction to Finance Textbook > Time Value of Money

Growing Annuities

PerpetuitiesPrevious Section
Growing PerpetuitiesNext Section
Popular Courses
Find My Course
0:00 / 0:00

Growing Annuities

A series of payments occurring over a finite period of time that increase by a constant percentage called the growth rate.
  • Present value is found using the first payment of the annuity, the effective rate, the growth rate, and the number of payments.
  • Present value is always one period before the first payment.

Present Value of a Growing Annuity

Present Value of a Growing Annuity (when r = g)

Future Value of a Growing Annuity

0:00 / 0:00

Example: Growing Annuities

You will receive the first of 10 payments next year. The first payment will be $200, and each of the following payments will increase by 5%. Using a discount rate of 8%, what is the present value of this cash flow?

Practice: Growing Annuities

Your sister has asked you to lend her money and has promised to repay you over 20 years. The first payment will be in one year, and each of the following payments will increase by 7%. How much is the first payment if your sister borrowed $60,000 from you at a rate of 9% compounded monthly?


0:00 / 0:00

Example: Growing Annuities

You will deposit the first of 10 payments next year into your savings account. The first payment will be $200, and each of the following payments will increase by 8%. Using a discount rate of 8%, what is the future value of this cash flow?

Practice: Growing Annuities

You just won a lottery that will pay you $1,000 in one year and 10% more each year thereafter for a total of 20 payments. What is the present value of your winnings if your opportunity cost is 10%?

Round your final answer to 2 decimal places.

Practice: Growing Annuities

You have decided to start saving for retirement. You plan to deposit $6,000 in 3 months into your retirement account which earns 12% interest compounded monthly, and 2% more each quarter. How much will you have saved up when you retire in 40 years?

Round the effective rate to at least 6 decimal places, and your final answer to the nearest dollar.
Extra Practice
You just borrowed money from your friend and have promised to pay them back over the next 15 years, with the first payment in one year. The first payment is going to be $1,600 and you will increase each annual payment by 4%. You both agreed to an APR of 6%, compounded weekly. How much did you borrow?
Round your final answer to 2 decimal places.
An annuity will pay the holder $500 at the end of the year and 10% more per year for a total of 20 payments. Assuming a discount rate of 10%, what is the present value of the annuity?
An annuity will pay the holder $500 at the end of the year and 8% more per year for a total of 20 payments. Assuming a discount rate of 10%, what is the future value of the annuity?
An annuity will pay the holder $500 at the beginning of the year and 8% more per year for a total of 20 payments. Assuming a discount rate of 10%, what is the present value of the annuity?
An annuity will pay the holder $500 at the end of the year and 8% more per year for a total of 20 payments. Assuming a discount rate of 10%, what is the future value of the annuity?
An annuity will pay the holder $500 at the end of the year and 10% more per year for a total of 20 payments. Assuming a discount rate of 10%, what is the present value of the annuity?
An annuity will pay the holder $500 at the end of the year and 8% more per year for a total of 20 payments. Assuming a discount rate of 10%, what is the present value of the annuity?
You've just borrowed money from your cousin and agreed to repay the loan in 10 instalments. The first payment, which you will pay one year from today, will be $500 and each payment thereafter will grow by 6%. The interest rate is 8% compounded bi-weekly. How much did you borrow?