Question

Derek will deposit $2,994.00 per year for 28.00 years into an account that earns 11.00%, The first deposit is made next year. How much will be in the account 39.00 years from today?

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#2

Derek will deposit $718.00 per year for 15.00 years into an account that earns 11.00%. The first deposit is made today. How much will be in the account 15.0 years from today? Note that he makes 15.0 total deposits.

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#3

Derek will deposit $503.00 per year into an account starting today and ending in year 18.00. The account that earns 15.00%. How much will be in the account 18.0 years from today?

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#4

Derek will deposit $3,974.00 per year for 25.00 years into an account that earns 11.00%, The first deposit is made next year. How much will be in the account 44.00 years from today?

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#5

Derek will deposit $4,650.00 per year for 25.00 years into an account that earns 11.00%, The first deposit is made next year. He has $14,169.00 in his account today. How much will be in the account 45.00 years from today?

Answer 1

1. Derek will deposit $2,994.00 per year for 28.00 years into an account that earns 11.00%, The first deposit is made next year. How much will be in the account 39.00 years from today?

Ans:

Future value for payment made at the end of the period = P ((1+r)ⁿ – 1)/r

Here , P= 2994

R= 11%

N= 28

FV= 2994*((1+0.11)^28 – 1 )/ 0.11

FV= 478,492.95

This is the future value at the end of 28^th year, so for the future value at the end of 38^th year or 39 years from today:

PV= 478,492.95

N= 10

R= 11%

FV= PV* (1+r)^n

FV= 478492.95* (1+0.11)^10

FV= $1,358,642.92

2. Derek will deposit $718.00 per year for 15.00 years into an account that earns 11.00%. The first deposit is made today. How much will be in the account 15.0 years from today? Note that he makes 15.0 total deposits.

Ans:

P= 718

N= 15

R= 11%

For future value of cash flows, made at the beginning of the period,

FV= P ((1+r)ⁿ – 1)/r * (1+r)

FV= (718((1+0.11)^15 – 1)/0.11 )*(1+0.11)

FV= $27420.38

3. Derek will deposit $503.00 per year into an account starting today and ending in year 18.00. The account that earns 15.00%. How much will be in the account 18.0 years from today?

Ans:

P= 503

N= 18

R= 15%

For future value of cash flows, made at the beginning of the period,

FV= P ((1+r)n – 1)/r * (1+r)

FV= (503((1+0.15)^18 – 1)/0.15 )*(1+0.15)

FV= $ 43,867.54

4. Derek will deposit $3,974.00 per year for 25.00 years into an account that earns 11.00%, The first deposit is made next year. How much will be in the account 44.00 years from today?

Ans:

Future value for payment made at the end of the period = P ((1+r)ⁿ – 1)/r

Here , P= 3974

R= 11%

N= 25

FV= 3974*((1+0.11)^25-1 )/ 0.11

FV= 454,678.48

This is the future value at the end of 25^th year, so for the future value at the end of 43^th year or 44 years from today:

PV= 454678.48

N= 18

R= 11%

FV= PV* (1+r)^n

FV= 454678.48*(1.11)^18

FV= $2,975,212.69