Question

Suppose you invest $25,000 at simple interest rate r. If you receive $1,250 in total interest after four years, what is the interest rate r?

Answer 1

Answer:

r = 0.012369

or

1.23686% rate

Step-by-step explanation:

Simple Interest Rate Formula: A = P(1 + r)ⁿ

A is your final amount.

P is your initial amount.

r is your rate.

n is the amount of time in years.

Step 1: Define variables

P = $25,000

n = 4 years

A = $25,000 + $1250 = $26,250

Step 2: Substitute known variables

26,260 = 25,000(1 + r)⁴

Step 3: Solve for rate r

Divide both sides by 25,000 1.0504 = (1 + r)⁴

Take the 4th root of both sides 1.01237 = 1 + r

Subtract 1 on both sides r = 0.012369

We have our answer r = 0.012369, but to find the percent rate, we multiply r by 100%:

0.012369 · 100% = 1.23686%

Answer 2

$\text{Hello!}$

$\large\boxed{1.25\%}$

$\text{Use the simple interest formula I = P * r * t where:}\\\\\text{I = amount of interest}\\\text{P = principle (initial amount)}\\\text{r = interest rate}\\\text{t = time period}\\\\\text{Substitute the known values from the problem:}\\\\1250 = 25000 * r * 4\\\\1250 = 100000r\\\\r = 0.0125\\\\\text{Convert to a percentage:}\\\\0.0125 * 100 = 1.25\%$