Question

An account was opened with $500 earning 8% simple interest. The account now has $980. How long hasthe account been open? Show your work for credit. The account has been open for 6 years

Answer 1

The account, opened with $500 and earning 8% simple interest, has a balance of $980. To determine the time, we used the simple interest formula I = Prt and discovered that it has been open for 12 years.

Step-by-step explanation:

The question involves calculating how long an account has been open based on the final amount in the account and the rate of simple interest applied to the initial deposit. Simple interest can be calculated using the formula I = Prt, where I represents the interest, P is the principal amount (initial amount), r is the annual interest rate expressed as a decimal, and t is the time in years.

We are given that the initial deposit was $500, the final amount is $980, and the annual interest rate is 8%. The interest earned then is $980 - $500 = $480. Using the formula, we get:

$480 = $500 × 0.08 × t

To find t, divide both sides by ($500 × 0.08):

t = $480 / ($500 × 0.08)

t = 480 / 40

t = 12 years

Therefore, the account has been open for 12 years, not 6 years as was incorrectly assumed in the question.

Answer 2

The formula to calculate Simple Interest is given as

`S\mathrm{}I\mathrm{}=\frac{\text{PRT}}{100}`

Where

S.I. = Simple Interest

P = Principal

R = Rate

T = Time

From the question,

S.I. = 980 - 500 = $480

P = $500

R = 8%

To find T,

`T=(100* S.I.)/(P* R)`

Substituting,

`\begin{gathered} T=(100*480)/(500*8) \\ T=(48000)/(4000) \\ T=12 \end{gathered}`

The account has been open for 12 years.