SOLUTION: It is now the beginning of the year. Assume that, starting at the end of the year, you will make deposits of $215 each year into a savings account. You will make a total of 11 year

Question 1118399: It is now the beginning of the year. Assume that, starting at the end of the year, you will make deposits of $215 each year into a savings account. You will make a total of 11 yearly deposits. Additionally, in 2 years your parents will give you a one-time gift worth $1522 which you will immediately deposit into your account.
If the savings account interest rate is 14%, what is the present value of this savings plan?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
the present value of annual deposits of 215 made at the end of each year for 11 years at 14% per year is equal to 1,172.3376.

in 2 years, your parents will give you a one time gift worth 1522.00 which you will immediately deposit into your account.

that would be at the end of year 2.

present value of that at 14% per year would be 1,171.129578.

add up 1,172.3376 and 1,171.129578 and you get a total present value of 2,343.467178 which can be rounded to 2,343.47.

the investment of 215 in year 1 is divided by 1.14^1.
the investment of 215 in year 2 is divided by 1.14^2.
etc..., until
the investment of 215 in year 12 is divided by 1.14^12.

the additional investment of 1522 in year 2 is divided by 1.14^2.

the sum of all these investments is the present value of the total.

this can be seen in the following excel printout.

$$$

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