Bridgette's grandparents opened a savings account for her and placed $500 in the account. The account pays 5.5% interest. Bridgette wants to be a singer and she has her heart set on a new karaoke machine. The machine costs $150. How much less will the account be worth in 8 years if she buys the karaoke machine now versus leaving the account untouched?
if left alone:
amount = 500(1.055)^8 = ....
if $150 is take out,
amount = 350(1.055)^8 - ...
take the difference between the two answers
To calculate the difference in the account worth, we need to find the future value of the account after 8 years with interest, and then subtract the cost of the karaoke machine.
Step 1: Calculate the future value of the account after 8 years with interest.
Future Value = Principal * (1 + Interest Rate)^Time
Principal = $500
Interest Rate = 5.5% = 0.055
Time = 8 years
Future Value = $500 * (1 + 0.055)^8
Using a calculator, we find that the future value of the account after 8 years is approximately $696.58.
Step 2: Calculate the difference in the account worth if she buys the karaoke machine now.
Account worth difference = Future Value - Cost of the karaoke machine
Account worth difference = $696.58 - $150
Calculating, we find that the account will be worth approximately $546.58 less in 8 years if Bridgette buys the karaoke machine now instead of leaving the account untouched.
To determine how much less the account will be worth in 8 years if Bridgette buys the karaoke machine now, we need to calculate the interest earned on the account over those 8 years and subtract the cost of the machine.
First, let's calculate the interest earned on the account. The interest rate is 5.5%, which means the account grows by that percentage each year.
To find the future value of the account after 8 years, we need to use the formula for compound interest:
Future Value = Principal * (1 + Interest Rate)^Number of Years
In this case, the principal (the initial amount in the account) is $500, the interest rate is 5.5%, and the number of years is 8.
Future Value = $500 * (1 + 0.055)^8
Now, let's calculate the future value of the account:
Future Value = $500 * (1.055)^8
Future Value ≈ $722.69
So, if Bridgette doesn't touch the account and lets it grow for 8 years, it will be worth approximately $722.69.
Now, let's calculate how much less the account will be worth if Bridgette buys the karaoke machine now. We need to subtract the cost of the machine ($150) from the future value of the account.
Lesser Value = Future Value - Cost of Karaoke Machine
Lesser Value = $722.69 - $150
Lesser Value ≈ $572.69
Therefore, the account will be worth approximately $572.69 less in 8 years if Bridgette buys the karaoke machine now instead of leaving the account untouched.