It's the first day of the year and you currently have $3,500 in the bank. You plan to deposit $600 at the end of every year for the next 58 years, with the first payment made 1 year from now (payments from t=1 to t=58 inclusive).If bank interest rates are 20% pa, how much money will be in your bank account a moment after making your last deposit in 58 years?Question 8Select one:a.$38,300b.$136,958,763.98c.$136,990,564.05d.$254,343,418.96e.$1,498,687,360.92
Question
It's the first day of the year and you currently have 600 at the end of every year for the next 58 years, with the first payment made 1 year from now (payments from t=1 to t=58 inclusive).If bank interest rates are 20% pa, how much money will be in your bank account a moment after making your last deposit in 58 years?Question 8Select one:a.136,958,763.98c.254,343,418.96e.$1,498,687,360.92
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 = $600, r = 20% = 0.20, and n = 58 years. So, the future value of the annuity is:
FV = $600 * [(1 + 0.20)^58 - 1] / 0.20
However, we also have an initial amount of $3,500 in the bank, which will also earn interest over the 58 years. The future value of this amount is given by the formula:
FV = PV * (1 + r)^n
where PV is the present value. In this case, PV = $3,500, so the future value of this amount is:
FV = $3,500 * (1 + 0.20)^58
The total amount in the bank account after 58 years is the sum of these two amounts.
After calculating these values, you will find that the correct answer is (c) $136,990,564.05.
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