Question

PLEASE HELP A GIRL OUT AND EXPLAIN

$800 is invested into an account that pays 1.6%, simple interest, for 5 weeks. Determine the total value of the account.

Answer 1

$864

Explanation:

1.6% simple interest means that the interest is always based off the starting amount. 1.6% of $800 is $12.8. The simple interest happens once every week (I think), so it will add $12.8 five times. 12.8 * 5 = 64, so the total amount added is 64 dollars. To find the total, we just added the two together. 800 + 64 = 864.

Answer 2

$801.23

Explanation:

You want the value of an account if $800 is invested at 1.6% simple interest for 5 weeks.

Simple interest

The formula for the value of the account is ...

A = P(1 +rt)

where P is the principal invested ($800), r is the annual interest rate (1.6%), and t is the number of years (5/52).

For the given numbers, the account value is ...

A = $800(1 +0.016·5/52) ≈ $801.23

The total value of the account is $801.23.

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Additional comments

In the formula, the decimal value of the interest rate is used. 1.6% = 0.016. The interest rate is usually taken to be an annual rate, unless otherwise specified. In modern times, it is not unusual for savings account interest rates to be 1% or less. (Many years ago, they were 5% or higher.)

Savings institutions may use different methods of computing short-term interest. A year length of 360 days is used to compute "ordinary interest." A year length of 365 days is used to compute "exact interest."

Here, the time period is specified in weeks, so we have used a year length of 52 weeks. The 5 week period is 5/52 years. The result is close to the value obtained for 35 days of "exact interest." If the ordinary interest computation is used, the account value would be $801.24.

It is tempting here to consider the 1.6% rate a weekly interest rate. That would correspond to an annual rate of about 128%, which would be an unusually high rate of interest.