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Annuities

Practice Problem Set 2

Future Value of an Annuity

1. On January 1, 2010, you put $1000 in a savings account that pays 61

4

% interest, and you will do

this every year for the next 18 [note this correction from the original problem] years withdraw

the balance on December 31, 2028, to pay for your child’s college education. How much will

you withdraw?

$1000 ×

(1 + .0625)18 − 1

. 0625

Present Value of an Annuity

2. On January 1, 2010, you win a lottery with a payoff of $2500 at the end of every year for the

next 10 years. If you discount the cash flow at 7.8%, what is the least amount you will accept as

a single payment right now, instead?

$2500 ×

1− (1 + .078)−10

. 078

Future Value of an Annuity Due

3. Suppose in Problem #1, above, you deposited the payments on the last day of each year instead

of the first (so you would deposit your last payment on December 31, 2028, then take all the

money out the same day)? How much will you withdraw in this case?

$1000 ×

(1 + .0625)17 − 1

. 0625

+ $1000

Present Value of an Annuity Due

4. Suppose in Problem #2, above, you receive your first payment right away. What is the

minimum amount you would take as a single payoff amount in this case?

$2500 ×

1− (1 + .078)−9

. 078

+ $2500

Annuities

Practice Problem Set 2

Future Value of an Annuity

1. On January 1, 2010, you put $1000 in a savings account that pays 61

4

% interest, and you will do

this every year for the next 18 [note this correction from the original problem] years withdraw

the balance on December 31, 2028, to pay for your child’s college education. How much will

you withdraw?

$1000 ×

(1 + .0625)18 − 1

. 0625

Present Value of an Annuity

2. On January 1, 2010, you win a lottery with a payoff of $2500 at the end of every year for the

next 10 years. If you discount the cash flow at 7.8%, what is the least amount you will accept as

a single payment right now, instead?

$2500 ×

1− (1 + .078)−10

. 078

Future Value of an Annuity Due

3. Suppose in Problem #1, above, you deposited the payments on the last day of each year instead

of the first (so you would deposit your last payment on December 31, 2028, then take all the

money out the same day)? How much will you withdraw in this case?

$1000 ×

(1 + .0625)17 − 1

. 0625

+ $1000

Present Value of an Annuity Due

4. Suppose in Problem #2, above, you receive your first payment right away. What is the

minimum amount you would take as a single payoff amount in this case?

$2500 ×

1− (1 + .078)−9

. 078

+ $2500