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Need help with this thank you

Need help with this thank you-example-1
User Stoner
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Answer:

see attached

Explanation:

You want the table filled in comparing account balances for 6% simple and compound interest over 4 years.

Simple interest formula

The balance of an account earning simple interest is ...

A = P(1 +rt)

where P is the initial amount invested, r is the annual interest rate, and t is the number of years.

Application

We have P = 7000 for both accounts. The 1-year formula becomes ...

A = P(1 +0.06·1) = 1.06P

The t-year formula for a principal of $7000 is ...

A = $7000(1 +0.06t)

Simple interest table

The first-year balance for the account earning simple interest is ...

A = 1.06($7000) = $7420

Each year, 6% of $7000 = $420 in interest is added to the account.

Compound interest table

The problem statement tells you to multiply each year's balance by the 1-year simple interest multiplier (1.06) to get the balance for the next year.

This means the year-4 balance in the compound interest account is ...

A = 1.06($8337.11) = $8837.34

Along the same lines, the year-2 balance will be found by dividing by that multiplier:

8837.11 = 1.06(year-2 balance)

year-2 balance = 8837.11/1.06 ≈ $7865.20

And the year-1 balance can be found the same way, or by matching the simple-interest number:

year-1 balance = $7865.20/1.06 = $7420 . . . from year-2 balance

year-1 balance = 1.06($7000) = $7420 . . . . . . same as simple interest

The filled-in table is attached.

Need help with this thank you-example-1
User Drejc
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