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, we need to find out how much money we are investing in the savings account and how much is left over for the bond and stock plan.
One-third of $15,000 is:
$15,000 / 3 = $5,000
So we have $5,000 to put into the savings account.
The remaining balance is:
$15,000 – $5,000 = $10,000
One-quarter of $10,000 is:
$10,000 / 4 = $2,500
So we have $2,500 to put into the U.S. Treasury bond. The rest, $7,500, will go into the stock plan.
To calculate the balance in the savings account after three years, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
where: A = the ending balance P = the principal (initial investment) r = the annual interest rate n = the number of times the interest is compounded per year t = the number of years
In this case, we have:
P = $5,000 r = 4.6% n = 1 (compounded annually) t = 3
Plugging these values into the formula, we get:
A = $5,000(1 + 0.046/1)^(1*3) A = $5,000(1.144516) A = $5,722.58
So the balance in the savings account after three years is $5,722.58.
