I would appreciate a clarification on the simple interest formula. I've come across two different formulas in different books
I've got
P+I=P(1+R)^n
Where P=Principal, I=Interest amount, R=Rate
and N=Total number of payment intervals=(Total duration of the loan in months)/Total duration of each compounding period in months
But I've also come across this formula
P+I=P(1+(R)/n)^n
Would like to confirm, which of the above are correct. Thanks
Compound Interest Formula
This topic has expert replies
-
- Junior | Next Rank: 30 Posts
- Posts: 19
- Joined: Sat Jul 30, 2011 10:39 pm
- Location: India
- Thanked: 3 times
Hi,
Both these formulas for Compound Intrest are correct but they are used in different situations.
Scenario1 P+I=P(1+R)^n
when intrest is compunded annually.
Scenario2 P+I=P(1+(R)/n)^n
When intrest is compunded quarterly or semi-annually.
For ex:if P=5000 and intrest is 10% compunded semi-annually(every 6 months)
Then interest will be 5% each every 6 months.
hence,I=$250 at the end of first six months and Amount will be $5250.
The Intrest for the next six months will be calculated for P=$5250 and Intrest rate=5%
Both these formulas for Compound Intrest are correct but they are used in different situations.
Scenario1 P+I=P(1+R)^n
when intrest is compunded annually.
Scenario2 P+I=P(1+(R)/n)^n
When intrest is compunded quarterly or semi-annually.
For ex:if P=5000 and intrest is 10% compunded semi-annually(every 6 months)
Then interest will be 5% each every 6 months.
hence,I=$250 at the end of first six months and Amount will be $5250.
The Intrest for the next six months will be calculated for P=$5250 and Intrest rate=5%
A note of caution: n is the number of compounding periods per year. For semi-annual compounding (6 months), n = 12/6 = 2. Similarly, n = 4 and 12 for quarterly and monthly compounding respectively.Touseef wrote:Hi,
Both these formulas for Compound Intrest are correct but they are used in different situations.
Scenario1 P+I=P(1+R)^n
when intrest is compunded annually.
Scenario2 P+I=P(1+(R)/n)^n
When intrest is compunded quarterly or semi-annually.
For ex:if P=5000 and intrest is 10% compunded semi-annually(every 6 months)
Then interest will be 5% each every 6 months.
hence,I=$250 at the end of first six months and Amount will be $5250.
The Intrest for the next six months will be calculated for P=$5250 and Intrest rate=5%
Hence, Future Value (at the end of one year) = $5000 * (1 + (10/2))^2 = $5512.50. Interest = FV - P = $512.50.
Last edited by edge on Sat Aug 06, 2011 12:12 pm, edited 2 times in total.
-
- Junior | Next Rank: 30 Posts
- Posts: 19
- Joined: Sat Jul 30, 2011 10:39 pm
- Location: India
- Thanked: 3 times
You are Right Edge.
But if u look closely you will observe that my logic is the same.
At the end of 6 months,I=$250 and the Amount will be $5250
For the next 6 months,$5250 will become the principal and 5% will be the intrest rate.
Hence,I=$262.5
Amount at the end of the year=5250+262.5=$5512.5
TOTAL ACCUMULATED INTREST=5512.5-5000=$512.5
But if u look closely you will observe that my logic is the same.
At the end of 6 months,I=$250 and the Amount will be $5250
For the next 6 months,$5250 will become the principal and 5% will be the intrest rate.
Hence,I=$262.5
Amount at the end of the year=5250+262.5=$5512.5
TOTAL ACCUMULATED INTREST=5512.5-5000=$512.5
-
- Master | Next Rank: 500 Posts
- Posts: 111
- Joined: Tue Dec 30, 2008 1:25 pm
- Location: USA
- Thanked: 28 times
- GMAT Score:770
It's easiest to use the variables t and m instead of n:
P + I = P(1 + r)^t with one compound per period and t periods.
P + I = P(1 + r/m)^(mt) with m compounds per period and t periods.
As an aside, when the limit of n to infinity is taken, the quantity (1 + 1/n)^n is equal to the mathematical constant e. We can show that when m compounds per period approaches a very high number, the interest formula approaches "continuous compounding", P + I = P*e^(rt):
P[1 + r/m]^(mt)
P[1 + 1/(m/r)]^[(mt)*(r/r)]
P[1 + 1/(m/r)]^[(m/r)(rt)]
Pe^(rt) (with the limit of m to infinity)
P + I = P(1 + r)^t with one compound per period and t periods.
P + I = P(1 + r/m)^(mt) with m compounds per period and t periods.
As an aside, when the limit of n to infinity is taken, the quantity (1 + 1/n)^n is equal to the mathematical constant e. We can show that when m compounds per period approaches a very high number, the interest formula approaches "continuous compounding", P + I = P*e^(rt):
P[1 + r/m]^(mt)
P[1 + 1/(m/r)]^[(mt)*(r/r)]
P[1 + 1/(m/r)]^[(m/r)(rt)]
Pe^(rt) (with the limit of m to infinity)
Compound interest is an interest calculated on both the principal and the current interest.
Formula:
For more details refer online math dictionary.
Formula:
For more details refer online math dictionary.