Question 384085: Interest Formulas
If you invest $P, and you earn interest only on the amount you invested (the $P), then ________________
interest is earned. If you invest $P and you earn interest not only on the $P, but also on the interest gained,
then ______________ interest is earned.
Let P = principal, r = annual nominal interest rate (in decimal form), t = time of the investment (in years), A
= amount in the account after t years. THEN…
Simple interest: A = _________________________________________
Compound interest: A = _____________________________________
Ideally, what do you want to happen to the value of n in the compound interest formula if the formula represented
the amount of money you have in the bank?
Found 2 solutions by mananth, Theo:
Answer by mananth(16946)   (Show Source):
You can put this solution on YOUR website! Interest Formulas
If you invest $P, and you earn interest only on the amount you invested (the $P), then _Simple interestis earned.
If you invest $P and you earn interest not only on the $P, but also on the interest gained,
then compound interest is earned.
Let P = principal, r = annual nominal interest rate (in decimal form), t = time of the investment (in years), A
= amount in the account after t years. THEN…
Simple interest: A = p*r*t+p
Compound interest: A = ____p(1+r/n)^nt____________________________________
Ideally, what do you want to happen to the value of n in the compound interest formula if the formula represented
the amount of money you have in the bank?
the more frequently you calculate the interest the more interest you earn
Answer by Theo(13342)  (Show Source):
You can put this solution on YOUR website! If you invest $P, and you earn interest only on the amount you invested (the $P), then SIMPLE interest is earned.
If you invest $P and you earn interest not only on the $P, but also on the interest gained, then COMPOUND interest is earned.
Let P = principal,
r = annual nominal interest rate (in decimal form),
t = time of the investment (in years),
A = amount in the account after t years. THEN…
SIMPLE INTEREST
A = P + (P * r * t)
Example:
P = 10,000
r = .10
t = 5 years
A = 10,000 + (10,000 * .10 * 5) = 10,000 + 5,000 = 15,000
COMPOUND INTEREST
A = P * (1+r)^t
Example:
P = 10,000
r = .10
t = 5 years
A = 10,000 * (1.10)^5 = 10,000 * 1.61051 = 16,1051
You make more money with compound interest than you do with simple interest, assuming the same investment in the same time frame with the same rate of return.
LAST QUESTION
Ideally, what do you want to happen to the value of n in the compound interest formula if the formula represented the amount of money you have in the bank?
I don't see "n" anywhere in your question.
If "n" is the number of compounding periods per year, than, ideally, you would want n to be as large as possible.
If n = 1, then the number of compounding periods per year is 1.
If n = 12, then the number of compounding periods per year is 12.
When n is greater than 1, you multiply the number of years by n and you divide the nominal interest rate by n.
The nominal interest rate is the annual interest assuming only 1 compounding period per year.
In the compounding example above, n was equal to 1 (not shown in the formula.
with n in the formula, the formula becomes:
A = P * (1 + (r/n))^(t*n)
When n was equal to 1, you got:
A = P * (1 + r) ^ n
That's what we solved earlier.
When n is 12, the formula becomes:
A = P * (1 + (r/12))^(t*12)
Same compounding example but with number of compounding periods per year equal to 12.
P = 10,000
r = .1
t = 5
r/12 = .1/12 = .008333333333
t*12 = 5*12 = 60
formula becomes:
A = 10,000 * (1.0083333333) ^ 60 = 16453.08934
with monthly compounding, the future value is 16,453.08934
with yearly compounding, the future value is 16,16,105.1
Your savings are greater when the number of compounding periods per year are greater.
The most compounding periods per year you can get is with continuous compounding.
That formula is A = P * e^rt)
e is the well known scientific constant of 2.718281828.....
Here you use the annual interest rate and the number of years.
You get:
A = 10,000 * e^(.1*5) = 10,000 * e^.5 = 16,487.21271
That's the theoretical maximum number of compounding periods per year.
If you compounded daily, you would get close to that.
Assume daily compounding with 365 days per year.
P = 10,000
i = .1 / 365 = .000273973
t = 5 * 365 = 1825
A = P * (1.000273973)^1825 = 16486.08362
That's pretty close to the theoretical maximum, but not exactly.
Bottom Line is the more the compounding periods per year, the greater your savings will be.
Without knowing what you meant by "n", this is the best I can come up with based on what I know about compounding.
I can't think of what else "n" can be, given the formulas as presented.
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