If someone gives you 10% interest on $1,000, then your account will have $100 added to it. If they give you the same amount of interest next year, you actually will earn a bit more than $100 in interest because you are now earning interest on $1,100 instead of $1,000.
1.
A bank account gives its depositors 5% interest of their average
balance throughout the year. A person has an average balance of $50,000
during the first year.
How much money do they have at the end of the first year?
To calculate their balance after the first year, we can calculate the interest they earn in the first year,
\[\$50,000 \cdot 0.05 = \$2,500\]
then add this total back to their starting balance.
\[\$50,000 + \$2,500 = \$52,500\]
A quicker way would be to multiply the starting balance by 1 + 0.05 = 1.05
\[\$50,000 \cdot 1.05 = \$52,500\]
2.
If they don’t add or subtract money from this total, and leave the
money into the next year, how much money do they have in their account
after the second year?
Their balance for the second year is \(\$52,500\). We increase this amount by 5%.
\[\$52,500 \cdot 1.05 =\$55,125\]
The first year earned $2,500 in interest. The second year earned $2,625 in interest!
3.
How much money will they have after ten years? A formula is used
in order to avoid the many calculations.
\[A = P(1 + r)^t\]
where \(A\) is the ending amount of money after \(t\) years, \(P\) is the starting amount, and \(r\) is the interest rate as a decimal. If we substitute \(P = 50000\), \(r = 0.05\), and \(t = 10\),
\[A = 50000(1 + 0.05)^{10}\]
\[A = 50000(1.05)^{10}\]
\[A \approx 50000(1.62889)\]
\[A \approx 81,444.73\]
If they collect 5% interest per year for 10 years, they will have earned \(31,444.73\) in interest.
4.
A person owes $2,000 on a credit card. The interest rate is 20%.
If they made no payments on the debt for 3 years, how much would they
owe after the third year (assuming interest is compounded yearly)?
We could use the above formula:
\[A = P(1 + r)^t\]
\[A = 2000(1 + 0.20)^3\]
\[A = 2000(1.20)^3\]
\[A = 2000(1.728)\]
\[A = 3456\]
1. A bank account gives its depositors 4% interest of their average balance throughout the year. A person has an average balance of $10,000 during the first year. How much money do they have at the end of the first year?
2. If they don’t add or subtract money from this total, and leave the money into the next year, how much money do they have in their account after the second year?
3. How much money will they have after ten years?
4. A person owes $5,000 on a credit card. The interest rate is 25%. If they made no payments on the debt for 3 years, how much would they owe after the third year (assuming interest is compounded yearly)?
1. How does compound interest help a person save for retirement? What should the person do to maximize their retirement savings?
2. How does the idea of compound interest help us understand debt?