# Thread: Annual Compound Interest Calculation: "How would years 3 and 4 appear in the above?"

1. ## Annual Compound Interest Calculation: "How would years 3 and 4 appear in the above?"

According to the information on compound interest at the following URL: http://www.moneychimp.com/articles/f...s/fmfutval.htm

"To find a formula for future value, We'll write P for your starting principal, and r for the rate of return expressed as a decimal. (So if the interest rate is 5%, r equals .05).
The balance will grow according to the following schedule:"

Year------------Balance

Now ------------P
1 ---------------P + rP
2---------------(P + rP) + r(P + rP)
3
4

How would years 3 and 4 appear in the above?

2. Originally Posted by KWF
According to the information on compound interest at the following URL: http://www.moneychimp.com/articles/f...s/fmfutval.htm

"To find a formula for future value, We'll write P for your starting principal, and r for the rate of return expressed as a decimal. (So if the interest rate is 5%, r equals .05).
The balance will grow according to the following schedule:"

Year------------Balance

Now ------------P
1 ---------------P + rP
2---------------(P + rP) + r(P + rP)
3--------------- (Previous balance) + r (Previous balance)
4--------------- (Previous balance) + r (Previous balance)

How would years 3 and 4 appear in the above?
.

3. 0: P(1 + r)^0 (that's NOW)
1: P(1 + r)^1
2: P(1 + r)^2
keep going...
n: P(1 + r)^n

4. Originally Posted by Subhotosh Khan
.
Would the following be correct? I want to see the (P + rP) or r(P + P) parts of the calculation used.

Year------------Balance

Now ------------P
1 ---------------P + rP
2---------------(P + rP) + r(P + rP)
3---------------(P + rP) + r(P +rP) + r(P +rP)
4---------------(P + rP) + r(P +rP) + r(P +rP) + r(P +rP)
5---------------etc.

5. Well then, using P=1000 and r=.10, balances will be:
0: 1000.00
1: 1100.00
2: 1210.00
3: 1331.00
4: 1464.10

Check your results; if you get above, yer correct!

6. Originally Posted by KWF
Would the following be correct? I want to see the (P + rP) or r(P + P) parts of the calculation used.

Year------------Balance

Now ------------P
1 ---------------P + rP
2---------------(P + rP) + r(P + rP)
3---------------(P + rP) + r(P +rP) + r(P +rP) .... Incorrect .... (P + rP) + r(P +rP) + r[(P +rP) +r(P+rP)]
4---------------(P + rP) + r(P +rP) + r(P +rP) + r(P +rP) .... Incorrect .... (P + rP) + r(P +rP) + r[(P +rP) +r(P+rP)] + r{(P + rP) + r(P +rP) + r[(P +rP) +r(P+rP)]}
5---------------etc.
.

7. rP = short for rePeat ?

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