Bermie deposited $ 4000 into an account that pays 45/a compounded quarterly during the first year. The interest rate on this account is then increased by o.2% each year. Calculate the balance in Bernie's account after three years.
"45/a compounded quarterly" ??
check your typing
oh sorry 45%/a
To calculate the balance in Bernie's account after three years, we need to calculate the compound interest for each year and add it to the initial deposit.
First, let's calculate the compound interest for the first year:
1. Convert the interest rate to decimal form: 45% = 0.45.
2. Calculate the interest rate for each quarter: 0.45 / 4 = 0.1125.
3. Calculate the balance at the end of the first year:
Initial deposit + (Initial deposit * interest rate) = $4000 + ($4000 * 0.1125) = $4000 + $450 = $4450.
Next, we need to calculate the balance for the next two years:
4. Increase the interest rate by 0.2% each year:
Year 2 interest rate = 0.45 + 0.2% = 0.452.
Year 3 interest rate = 0.452 + 0.2% = 0.4542.
5. Calculate the balance at the end of the second year:
Balance at the end of the first year + (Balance at the end of the first year * interest rate) = $4450 + ($4450 * 0.452) = $4450 + $2014.60 = $6464.60.
6. Calculate the balance at the end of the third year:
Balance at the end of the second year + (Balance at the end of the second year * interest rate) = $6464.60 + ($6464.60 * 0.4542) = $6464.60 + $2936.35 = $9400.95.
Therefore, Bernie's account will have a balance of $9400.95 after three years.