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Solution - Compound interest (basic)

481089.31

481089.31

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Step-by-step explanation

1. Parse compound interest input

$c i (22560, 12, 1, 27)$

Operation detected: compound interest basic.

$c i (22560, 12, 1, 27)$

Read the input parameters and label them as $P, r, n, t$ .

$P = 22560, r = 12 %, n = 1, t = 27$

$\frac{12}{100} = 0.12$

Use the standard compound-interest model with periodic compounding.

$A = P {(1 + r / n)}^{(n t)}$

Plan: compute periodic rate and number of periods, then evaluate the growth factor.

$N e x t c o m p u t e r / n, n t, a n d {(1 + r / n)}^{(n t)} .$

Parse the input values as $P = 22, 560$ , $r = 12 %$ , $n = 1$ , and $t = 27$ ; then select $A = P {(1 + r / n)}^{(n t)}$ .

2. Compute period rate and growth factor

$\frac{r}{n} = 0.12$

$n t = 27$

${(1 + r / n)}^{(n t)}$

Substitute the computed values into the growth-factor expression.

${(1 + r / n)}^{(n t)}$

${(1 + 0.12)}^{27} = 21.3248807917$

The growth factor is ready; now multiply by the principal.

$21.3248807917$

Convert annual rate to decimal, compute $\frac{r}{n}$ and $n t$ , then evaluate ${(1 + r / n)}^{(n t)}$ .

3. Conclude final amount

$A = 481089.31$

$481089.31$

Conclusion: this is the accumulated amount after compounding.

$481089.31$

Study tip: keep rate and time units consistent (annual rate with periods per year).

$481089.31$

Multiply the principal by the growth factor to get the final amount $A$ .

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Compound interest appears in savings, loans, and investments. Understanding it builds strong financial literacy.

Terms and topics

Compound interest (basic)

Solution - Compound interest (basic)

Step-by-step explanation

1. Parse compound interest input

2. Compute period rate and growth factor

3. Conclude final amount

Why learn this

Terms and topics

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