The sooner you start to save, the more you'll earn with compound interest.
How compound interest works
Compound interest is the interest you get on:
- the money you initially deposited, called the principal
- the interest you've already earned
For example, if you have a savings account, you'll earn interest on your initial savings and on the interest you've already earned. You get interest on your interest.
This is different to simple interest. Simple interest is paid only on the principal at the end of the period. A term deposit usually earns simple interest.
Save more with compound interest
The power of compounding helps you to save more money. The longer you save, the more interest you earn. So start as soon as you can and save regularly. You'll earn a lot more than if you try to catch up later.
For example, if you put $10,000 into a savings account with 3% interest compounded monthly:
- After five years, you'd have $11,616. You'd earn $1,616 in interest.
- After 10 years you'd have $13,494. You'd earn $3,494 in interest.
- After 20 years you'd have $18,208. You'd earn $8,208 in interest.
Compound interest formula
To calculate compound interest, use the formula:
A = P x (1 + r)n
A = ending balance
P = starting balance (or principal)
r = interest rate per period as a decimal (for example, 2% becomes 0.02)
n = the number of time periods
How to calculate compound interest
To calculate how much $2,000 will earn over two years at an interest rate of 5% per year, compounded monthly:
1. Divide the annual interest rate of 5% by 12 (as interest compounds monthly) = 0.0042
2. Calculate the number of time periods (n) in months you'll be earning interest for (2 years x 12 months per year) = 24
3. Use the compound interest formula
A = $2,000 x (1+ 0.0042)24
A = $2,000 x 1.106
A = $2,211.64
Lorenzo and Sophia compare the compounding effect
Lorenzo and Sophia both decide to invest $10,000 at a 5% interest rate for five years. Sophia earns interest monthly, and Lorenzo earns interest at the end of the five-year term.
After five years:
- Sophia has $12,834.
- Lorenzo has $12,500.
Sophia and Lorenzo both started with the same amount. But Sophia gets $334 more interest than Lorenzo because of the compounding effect. Because Sophia is paid interest each month, the following month she earns interest on interest.
This question was previously asked in
SSC CGL Tier-II Quant Previous Paper 18 (Held On: 30 November 2016)
View all SSC CGL Papers >
- Rs. 1856.40
- Rs. 1600
- Rs. 1856
- Rs. 1756.60
Answer (Detailed Solution Below)
Option 1 : Rs. 1856.40
Free
10 Questions 10 Marks 7 Mins
P = 4000, r = 10% and time = 4 years
As we know,
CI = P [(1 + r/100)t - 1]
CI = 4000 [1 + 10/100)4 - 1]
CI = 4000 [(11/10)4 - 1]
CI = 4000 [14641/10000 - 1]
CI = 4000 × 4641/10000
∴ CI = 1856.4
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Let's discuss the concepts related to Interest and Compound Interest. Explore more from Quantitative Aptitude here. Learn now!
Find compound interest on RS 4000 at10% per annum for 2 years and 3 months, compounded annually
A. 921
B. 491
C. 961
D. 941
Answer: Option C
Solution(By Examveda Team)
Principal(P) = Rs 4000
Rate of Interest(r ) = 10%
Time = 2 years and 3 months
Here first we take n = 2 years.
A = P( 1 + r /100)n Where A =
Amount and n = number of years
A = 4000 (11/10)2
A = 4000 ( 121 / 100 )
A = Rs 4840
The Amount after two years = Rs 4840
Now Principal = Rs 4840
Simple interest for last 3 month i.e 1/4 year is = PRT/100 = (4840 × 10 × 1 / 4) / 100 = Rs.121
Amount after 2 years and 3 months = Rs 4840 + Rs 121 = Rs 4961
C.I = A - P
C.I = 4961 - 4000 = Rs. 961
∴ The compound interest is Rs. 961