Calculating Balance of Savings Account
You save $15,000.00. You place one-third in a savings account earning a 4.6% APR compounded annually. You then invest one quarter of the remaining balance in a 3-year U.S. Treasury bond earning a 5.2% APR compounded annually and the rest in a stock plan. Your stock plan increases in value 3% the first year, decreases 8% in value the second year, and increases 6% in value the third year. What is the balance of the savings account by the end of the third year?
First, let’s calculate how much money is placed in the savings account:One-third of $15,000.00 is:
$15,000.00 * (1/3) = $5,000.00
Next, let’s calculate how much money is left after $5,000.00 is placed in the savings account:
$15,000.00 – $5,000.00 = $10,000.00
One-quarter of $10,000.00 is:
$10,000.00 * (1/4) = $2,500.00
The remaining balance that is invested in the stock plan is:
$10,000.00 – $2,500.00 = $7,500.00
Now, let’s calculate the balance of the savings account after 3 years. We’ll use the formula for compound interest:
A = P(1 + r/n)^(nt)
where:
A = the balance after 3 years P = the initial principal (the amount invested in the Treasury bond) r = the annual interest rate (5.2%) n = the number of times the interest is compounded in a year (once annually) t = the number of years (3 years)
Plugging in the values, we get:
A = $2,500.00(1 + 0.052/1)^(1*3) = $2,938.42
A = the balance after 3 years P = the initial principal (the amount placed in the savings account) r = the annual interest rate (4.6%) n = the number of times the interest is compounded in a year (once annually) t = the number of years (3 years)
Plugging in the values, we get:
A = $5,000.00(1 + 0.046/1)^(1*3) = $5,875.56
So the balance in the savings account at the end of the third year is $5,875.56.
Next, let’s calculate the value of the Treasury bond after 3 years. We’ll use the same formula:
A = P(1 + r/n)^(nt)
