bank deposit, future value problem

[hcc221]

You have $500 in the bank today, and assume the interest rate is always 5% per year. You plan to deposit an additional $1000 per year for 8 years, with the first of those new deposits being made 1 year from today. How much will you have in the bank after 8 years?

answer: 10,287.83


how do i solve this?

 

[Denis]

10,287.83 is correct.

Calculate future value of 500 ...easy, right?
Calculate future value of 8 deposits of 1000 ... ok?
Add 'em up!

 

[hcc221]

10,287.83 is correct.

Calculate future value of 500 ...easy, right?
Calculate future value of 8 deposits of 1000 ... ok?
Add 'em up!

i'm not getting that answer, i'm getting something around there

for the first FV of 500, i got 525
for the second FV, i got 9549.18

total is 10,074.18...what am i doing wrong?

 

[Denis]

for the first FV of 500, i got 525

That's future value after 1 year ; 500 * 1.05 = 525

You need it after 8 years: 500 * 1.05^8 = ~738.73

You can look at these as 2 separate bank accounts:
1: one in which you deposit $500 now and leave it untouched for 8 years
2: one in which you deposit $1000 each year for 8 years, beginning in 1 year
Kapish?

You can also treat the 2nd account as 8 accounts:
1: 1000 for 7 years
2: 1000 for 6 years
....
7: 1000 for 1 year
8: 1000 for 0 years
So future value = 1000(1.05^7) + 1000(1.05^6) .... + 1000(1.05^1) + 1000(1.05^0) = ~9549.11

The formula 1000(1.05^8 - 1) / .08 is simply the addition of the above. Understand?

Year     Deposit   Interest   Balance
0         500.00               500.00
1        1000.00    25.00     1525.00  (500 * .05 = 25.00)
2        1000.00    76.25     2601.25  (1525 * .05 = 76.25)

This is what a "bank statement" of the actual account will look like.
Do the next 6 years similarly and you'll end up with the answer to your problem.