If I invested $174.80 every month at a rate of 6%compounded monthly for 25 years, how would I figure out the?

Question

How do I figure out how much the investment is worth at the end of the 25 years. Thank you.

Answer 1

I use MS Excel.
Use 1 column for the date, 1 for the amount invested, 1 for monthly earnings, and 1 for the balance.
Earnings = previous months balance * 0.5% (6% annual rate / 12 months).
New balance = Old balance + investment + earnings.
I come up with $121,741.02.

Answer 2

This problem can be solved with some relatively simple algebra. There are 300 months in 25 years and the monthly interest rate is 6%/12 = 0.5% = .005. Furthermore, an investment of $174.80 compounded monthly for n months is worth $174.80 * (1.005) ** n after n months

- The $174.80 you invest at the beginning of month one is worth $174.80 * (1.005) ** 300 at the end of the 300 months
- The $174.80 you invest at the beginning of month two is worth $174.80 * (1.005) ** 299 at the end of the 300 months.
.
.
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- The $174.80 you invest at the beginning of month 300 is worth $174.80 * (1.005) at the end of the 300 months.

This means that the calculation needed is

$174.80 * (1.005**300 + 1.005**299 + 1.005**298 + ... 1.005)

At first glance it appears that it will be necessary to calculate 1.005 raised to 300 different powers and add the results together, then multiply by $174.80. Fortunately, the expression inside the parentheses simplifies into

1.005 * (1.005**300 - 1) / (1.005 - 1) = 696.4589322

Therefore if you invest $174.80 every single month for 25 years and get exactly 6% interest compounded monthly, at the end of 25 years the value of your investment will be more than 696 times the amount of your $174.80 monthly investment and be worth $121,741.02

Answer 3

You need to use a compound interest calculator for this one. I put your numbers in the calculator and got $122,521.50

note: where it says "annual addition, i put $2097.60 which is your $174.80 times 12 months, and then where it says "compound ___ times annually" put 12.

Answer 4

All the equations can be found in a book like this at the library, dewey decimal number 658.15

http://www.amazon.com/Contemporary-Engineering-Economics-Chan-Park/dp/0130893102

Answer 5

I got $121,741.02 using those figures
$52,440 is the money directly saved the rest is interest earned .