It's the first day of the year and you currently have $3,000 in the bank. You plan to deposit $800 at the end of every year for the next 55 years, with the first payment made 1 year from now (payments from t=1 to t=55 inclusive).If bank interest rates are 11% pa, how much money will be in your bank account a moment after making your last deposit in 55 years?Question 8Select one:a.$933,007.4b.$940,256.74c.$2,871,685.4d.$3,187,570.79e.$14,617,115.92
Question
It's the first day of the year and you currently have 800 at the end of every year for the next 55 years, with the first payment made 1 year from now (payments from t=1 to t=55 inclusive).If bank interest rates are 11% pa, how much money will be in your bank account a moment after making your last deposit in 55 years?Question 8Select one:a.940,256.74c.3,187,570.79e.$14,617,115.92
Solution
To solve this problem, we need to use the formula for the future value of an ordinary annuity and the formula for compound interest.
The future value of an ordinary annuity formula is:
FV = P * [(1 + r)^n - 1] / r
Where: FV = Future Value P = Payment per period (in this case, per year) r = Interest rate per period (in this case, per year) n = Number of periods (in this case, number of years)
First, we calculate the future value of the annuity (the yearly deposits):
FV = 2,871,685.4
Next, we calculate the future value of the initial deposit using the compound interest formula:
FV = P * (1 + r)^n
FV = 315,885.39
Finally, we add these two amounts together to find the total amount in the bank account after 55 years:
315,885.39 = $3,187,570.79
So, the correct answer is d. $3,187,570.79.
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