Your parents open a bank account for you when you were born. They deposit $16,000.00 into the account.The account generates 9.9% per annum for 7 years, then 6.2% per annum for 6 years, then 11.7% per annum for 5 years.How much money is there in the account when you reach the age of 18?Round your final answer to 2 decimal places. E.g. if the final answer is $12345.8342, please type 12345.83 in the answer box (do not type the dollar sign).
Question
Your parents open a bank account for you when you were born. They deposit 12345.8342, please type 12345.83 in the answer box (do not type the dollar sign).
Solution
To solve this problem, we need to use the formula for compound interest, which is A = P(1 + r/n)^(nt), where:
- A is the amount of money accumulated after n years, including interest.
- P is the principal amount (the initial amount of money).
- r is the annual interest rate (in decimal).
- n is the number of times that interest is compounded per year.
- t is the time the money is invested for in years.
In this case, interest is compounded once per year (n=1), and the principal amount is $16,000. The interest rate and time change three times.
Here are the steps to solve the problem:
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Calculate the amount after 7 years with an interest rate of 9.9% per annum: A = 30,992.89
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The amount after 7 years becomes the principal for the next 6 years. Calculate the amount after the next 6 years with an interest rate of 6.2% per annum: A = 41,643.59
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The amount after 13 years (7+6) becomes the principal for the next 5 years. Calculate the amount after the next 5 years with an interest rate of 11.7% per annum: A = 73,487.03
So, when you reach the age of 18, there will be approximately $73,487.03 in the account.
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