Compound Interest is calculated on the initial payment and also on the interest of previous periods.
Example: Suppose you give \$100 to a bank which pays you 10% compound interest at the end of every year. After one year you will have \$100 + 10% = \$110, and after two years you will have \$110 + 10% = \$121.
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Problem
If you deposit $4300 into an account paying 9% annual interest compounded quarterly, how long until there is $2720 in the account?
Result
It wil take approximately 10 months and 8 days for the account to go from $4300 to $2720.
Explanation
To find time we use formula:
$$ A = P \left( 1 + \frac{r}{n} \right)^{\Large{n \cdot t}} $$ |
A = total amount P = principal or amount of money deposited, r = annual interest rate n = number of times compounded per year t = time in years |
In this example we have
$$ A = \$2720 ~,~ P = \$4300 , r = 9\% ~~ \text{and} ~ n = 4$$After plugging the given information we have
$$ \begin{aligned} 2720 &= 4300 \left( 1 + \frac{ 0.09 }{ 4 } \right)^{\Large{ 4 \cdot t }} \\ 2720 &= 4300 \cdot {( 1.0225 )} ^ { \Large{ 4 \cdot t } } \\ { (1.0225) } ^ { \Large{ 4 \cdot t } } &= \frac{ 2720 }{ 4300 } \\ { (1.0225) } ^ { \Large{ 4 \cdot t } } &= 0.63256 ~~ \text{Take the natural logarithm of both sides} \\ \ln \left({ 1.0225 } ^ { \Large{ 4 \cdot t } } \right) &= ln \left( 0.63256 \right) \\ 4 \cdot t \cdot ln \left( 1.0225 \right) &= ln \left( 0.63256 \right) \\ 4 \cdot t &= \frac{ ln \left( 0.63256 \right) }{ ln \left( 1.0225 \right) } \\ 4 \cdot t &= -20.58282 \\ t &= -5.1457 ~ \text{years}= \text{ 10 months and 8 days } \end{aligned}$$Share this result with others by using the link below.
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This is a list of the example problems which can be solved by using this calculator.
Example 1: What will a deposit of \$4,500 at 7% compounded yearly interest be worth if left in the bank for 9 years?
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Example 2: What will a deposit of $3,500 at 10% compounded monthly be worth if left in the bank for 8 years?
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Example 3: How much money would you need to deposit today at 8% annual interest compounded monthly to have \$1200 in the account after 12 years?
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Example 4: Find the present value of \$1,000 to be received at the end of 2 years at a 12% nominal annual interest rate compounded quarterly.
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Example 5: What annual interest rate is implied if you lend someone $1,700 and are repaid $1,910 in two years?
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Example 6: Suppose that a savings account is compounded monthly with a principal of \$1350. After 8 months, the amount increased to \$1424. What was the per annum interest rate?
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Example 7: How long does it take for \$4,300 to grow into \$2,720 at 9% compounded quarterly?
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