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.