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Suppose you received a gift of $10,000 and want to invest it. You visit two banks to see what they have to offer. Bank A is near your home and pays 5% interest compounded annually. Bank B is farther from your home and pays 6% interest compounded annually. You do not think a 1% difference in rates is that significant, but you want to check.
Calculate the amount of interest each plan will earn after one year. Record your answers on the lines provided.

If the initial amount (also called as principal amount) is P, and the interest rate is R% per unit time, and it is left for T unit of time for that compound interest, then the interest amount earned is given by:

[tex]CI = P(1 +\dfrac{R}{100})^T - P[/tex]

The final amount becomes:

[tex]A = CI + P\\A = P(1 +\dfrac{R}{100})^T[/tex]

For bank A:

P = initial deposit amount = $10,000
R = rate of interest = 5% annually (so here unit of time is 1 year).
T = units of time for which investment occurs = 1 year

Thus, the amount after 1 year would be:

[tex]CI_A = P(1 +\dfrac{R}{100})^T -P= 10000(1 +\dfrac{5}{100})^1 - 10000 = 500 \: \rm dollars[/tex]

For bank B:

P = initial deposit amount = $10,000
R = rate of interest = 6% annually (so here unit of time is 1 year).
T = units of time for which investment occurs = 1 year

Thus, the amount after 1 year would be:

[tex]CI_B = P(1 +\dfrac{R}{100})^T -P= 10000(1 +\dfrac{6}{100})^1 - 10000 = 600 \: \rm dollars[/tex]

Thus, the amount of interest each plan will earn after one year is $500 for bank A, and $600 for bank B.

Learn more about compound interest here:

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