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A bank has launched a three-year structured deposit that offers an effective annual interest of 8% for the first 18 months, quarterly interest of 1.5% for the next 6 months and semi-annual interest of 2% for the last 12 months. If I wish to receive $100, 000 on the maturity date (that is, on the last day of the third year), how much, to the nearest dollar, should I invest? (Assume that interest rates and principal are guaranteed)

User Nikolay
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Answer:

To determine how much you should invest to receive $100,000 on the maturity date, you will need to calculate the present value of the cash flows at the beginning of the investment. The present value is the amount of money you would need to invest today to receive a certain amount at a future date, taking into account the time value of money and the interest rate.

You can calculate the present value by using the formula:

PV = CF / (1 + r)^t

Where:

PV = present value

CF = cash flow (the amount you will receive at the maturity date)

r = interest rate

t = time (in years)

The first 18 months, the interest rate is 8% per year, which is equivalent to 8/12 = 0.67% per month.

The next 6 months, the interest rate is 1.5% per quarter, which is equivalent to 1.5/4 = 0.375% per month.

The last 12 months, the interest rate is 2% per semi-annual, which is equivalent to 2/2 = 1% per month.

For the first 18 months, the present value of the cash flow is:

PV = 100,000 / (1 + 0.0067)^(18/12) = 95,167

For the next 6 months, the present value of the cash flow is:

PV = 95,167 / (1 + 0.00375)^(6/12) = 94,853

For the last 12 months, the present value of the cash flow is:

PV = 94,853 / (1 + 0.01)^(12/12) = 94,853

So, to receive $100,000 on the maturity date, you should invest 94,853 dollars to the nearest dollar.

User Rwitzel
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