Problem #3: Initially. S60.000 is put into an investment account. Three months l

Question

Problem #3: Initially. S60.000 is put into an investment account. Three months later. S6.000 is withdrawn. Two years after the initial investment, the account is worth S59901.72. Assuming a dollar-weighted method for the first year, and a time-weighted method for the second year, the effective annual interest rate was equal to the same value each year. What is that value? Answer as a percentage, correct to 2 decimals. Problem #3: ve l submit Problem #3 for Problem #3 Your Answer: Your Mark: Attempt #1 Attempt #2 Attempt #3 Attempted Attempt #5

Explanation / Answer

Let Y = account value after 1 year of the initial deposit of $60,000 and x = effective annual interest rate

Thus for the 1sy year (dollar weighted) x = (y-60,000+6,000)/(60,000-6,000*(1-3/12)

Or x = y – 54,000/55,500 (equation 1)

For 2nd year (time weighted), 59901.72/y = 1+x

Or x = 59901.81/y – 1 (equation 2)

As x = equation 1 = equation 2

y – 54,000/55,500 = 59901.81/y – 1

or y = 56,913.79

From equation 2 we get x = 59901.81/y – 1

Or x = (59901.81/56913.79) – 1

= 1.0525 – 1

= 0.0525

= 5.25%

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