It's the first day of the year and you currently have $3,500 in the bank. You plan to deposit $400 at the end of every year for the next 51 years, with the first payment made 1 year from now (payments from t=1 to t=51 inclusive).If bank interest rates are 13% pa, how much money will be in your bank account a moment after making your last deposit in 51 years?Question 8Select one:a.$3,346,757.8b.$2,961,732.57c.$1,564,097.22d.$23,900e.$6,570.88
Question
It's the first day of the year and you currently have 400 at the end of every year for the next 51 years, with the first payment made 1 year from now (payments from t=1 to t=51 inclusive).If bank interest rates are 13% pa, how much money will be in your bank account a moment after making your last deposit in 51 years?Question 8Select one:a.2,961,732.57c.23,900e.$6,570.88
Solution
To solve this problem, we need to calculate the future value of a series of cash flows, which is a typical problem in financial mathematics. The formula for the future value of an ordinary annuity is:
FV = P * [(1 + r)^n - 1] / r
where:
- FV is the future value of the annuity,
- P is the amount of each payment,
- r is the interest rate per period, and
- n is the number of periods.
In this case, P = $400, r = 13% = 0.13, and n = 51 years. So, the future value of the annuity is:
FV = $400 * [(1 + 0.13)^51 - 1] / 0.13
However, we also have an initial amount of $3,500 in the bank, which will also earn interest over the 51 years. The future value of this amount is:
FV = $3,500 * (1 + 0.13)^51
The total amount in the bank account after 51 years will be the sum of these two amounts.
Let's calculate these values:
FV_annuity = 2,961,732.57 FV_initial = 385,025.23
Total = FV_annuity + FV_initial = 385,025.23 = $3,346,757.8
So, the correct answer is a. $3,346,757.8.
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