Compound interest
key notes:
B = p(1 + r)t
where,
B is the balance (final amount).
p is the principal (starting amount).
r is the interest rate expressed as a decimal.
t is the time in years.
note: The interest is the balance minus the principal.
Learn with an example
Diego deposited ₹100 in a savings account earning 12% interest, compounded annually.
To the nearest paisa,
how much will he have in 1 year?
Write the rate as a decimal.
12% = 0.12
Calculate the balance.
| B | = | p(1 + r)t |
| = | ₹100(1 + 0.12)1 | |
| = | ₹100(1.12)1 | |
| = | ₹100(1.12) | |
| = | ₹112 |
The balance will be ₹112.
Lindsey deposited ₹200 in a savings account earning 7% interest, compounded annually.
To the nearest paisa,
how much interest will she earn in 3 years?
Write the rate as a decimal.
7% = 0.07
Calculate the balance.
| B | = | p(1 + r)t |
| = | ₹200(1 + 0.07)3 | |
| = | ₹200(1.07)3 | |
| = | ₹200(1.225043) | |
| = | ₹245.0086 |
Now use this to find the interest, which is the balance minus the principal.
₹245.0086 − ₹200 = ₹45.0086
Round to the nearest paisa.
₹45.0086 → ₹45.01
To the nearest paisa, the interest will be ₹45.01.
Norma has ₹50 in a savings account. The interest rate is 6%, compounded annually.
To the nearest paisa,
how much interest will she earn in 3 years?
Use the formula B = p(1 + r)t, where B is the balance (final amount), p is the principal (starting amount), r is the interest rate expressed as a decimal, and t is the time in years. ₹_____
Write the rate as a decimal.
6% = 0.06
Calculate the balance.
| B | = | p(1 + r)t |
| = | ₹50(1 + 0.06)3 | |
| = | ₹50(1.06)3 | |
| = | ₹50(1.191016) | |
| = | ₹59.5508 |
Now use this to find the interest, which is the balance minus the principal.
₹59.5508 − ₹50 = ₹9.5508
Round to the nearest paisa.
₹9.5508 → ₹9.55
To the nearest paisa, the interest will be ₹9.55.
Let’s Practice!
