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Compound interest calculator
Compound interest is calculated on both the initial payment, and the interest earned in previous periods.
problem
If you deposit $0 into an account paying 0% annual interest compounded yearly. Find the amount and interest after 0 ?
solution
The amount is $0 and the interest is $0.
explanation
STEP 1: Convert 0 into years.
STEP 2: To find amount we use formula:
| $$ A = P \left( 1 + \frac{r}{n} \right)^{\Large{n \cdot t}} $$ |
A = total amount P = principal (amount of money deposited) r = annual interest rate n = number of times compounded per year t = time in years |
In this example we have
$$ P = \$0 ~,~ r = 0 \% ~ , ~ n = 1 ~ \text{and} ~ t = 0 ~ \text{years}$$After plugging the given information we have
$$ \begin{aligned} A &= 0 \left( 1 + \frac{ 0 }{ 1 } \right)^{\Large{ 1 \cdot 0 }} \\ A &= 0 \cdot { 1 } ^ { 0 } \\ A &= 0 \cdot 1 \\ A &= 0 \end{aligned} $$STEP 3: To find interest we use formula $ A = P + I $, since $ A = \$0 $ and $ P = \$0 $ we have:
$$ \begin{aligned} A &= P + I \\ 0 &= 0 + I \\ I &= 0 - 0 \\ I &= 0 \end{aligned}$$close
working...
Examples
ex 1:
What is the value of a $4500 deposit at 7% compounded annual interest if it is held in a
bank for 9 years?
ex 2:
What will a $3500 deposit at 10% compounded
monthly be worth after 8 years in the bank?
ex 3:
How much money would you need to put today at 8% annual
compounded monthly
interest to have $1200 in the account after 12 years?
ex 4:
Determine the present value of $1000 at a 12% annual interest rate compounded
quarterly at the end of two years.
ex 5:
What is the estimated yearly interest rate if you give someone
$1700 and get repaid
$1910 in two years?
ex 6:
Assume that a savings account with a principal of $1350 is
compounded monthly.
After 8 months, the total had risen to $1424. What was the interest rate per year?
ex 7:
How long does it take $4300 to grow to $6720 when compounded quarterly at
9%?
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