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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)

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Answer: To the nearest dollar, you should invest $84,639

Step-by-step explanation:

First, we need to calculate the number of compounding periods in a year.

For the first 18 months, the compounding period is monthly, so there are 18 x 12 = 216 compounding periods

For the next 6 months, the compounding period is quarterly, so there are 6 x 4 = 24 compounding periods

For the last 12 months, the compounding period is semi-annual, so there are 12 x 2 = 24 compounding periods

The total number of compounding periods is 216 + 24 + 24 = 264

Next, we need to calculate the effective annual interest rate for the entire 3-year period.

The effective annual interest rate is (1 + (8%/216))^216 x (1 + (1.5%/24))^24 x (1 + (2%/24))^24 - 1

Now we can calculate the principal amount (P) required to achieve the desired maturity value (F) using the formula:

P = F / (1 + r)^n

where F is the maturity value, r is the effective annual interest rate and n is the number of compounding periods

P = 100,000 / (1 + r)^264

Explanation: To receive $100,000 on the maturity date, the principal amount has to be invested such that it earns the effective annual interest rate for the entire 3-year period. The principal amount was calculated using the formula for future value of an investment, where the maturity value, effective annual interest rate and the number of compounding periods are known.