It's the first day of the year and you currently have $3,000 in the bank. You plan to deposit $200 at the end of every year for the next 54 years, with the first payment made 1 year from now (payments from t=1 to t=54 inclusive).If bank interest rates are 21% pa, how much money will be in your bank account a moment after making your last deposit in 54 years?Question 8Select one:a.$88,620,851.57b.$88,630,699.22c.$116,752,248.18d.$141,270,220.3e.$407,651,536.41
Question
It's the first day of the year and you currently have 200 at the end of every year for the next 54 years, with the first payment made 1 year from now (payments from t=1 to t=54 inclusive).If bank interest rates are 21% pa, how much money will be in your bank account a moment after making your last deposit in 54 years?Question 8Select one:a.88,630,699.22c.141,270,220.3e.$407,651,536.41
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 (FV) of an ordinary annuity formula is:
FV = P * [(1 + r)^n - 1] / r
Where: P = annuity payment ($200) r = interest rate (21% or 0.21) n = number of periods (54 years)
So, the future value of the annuity payments is:
FV = 200 * [(1 + 0.21)^54 - 1] / 0.21
Next, we need to calculate the future value of the initial $3,000 deposit using the compound interest formula:
FV = P * (1 + r)^n
Where: P = principal amount ($3,000) r = interest rate (21% or 0.21) n = number of periods (54 years)
So, the future value of the initial deposit is:
FV = 3000 * (1 + 0.21)^54
Finally, we add these two amounts together to get the total amount in the bank account after 54 years.
Please note that the actual calculations would require a calculator or software capable of handling such large exponents. The answer should be one of the options provided.
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