You have some money on deposit in a bank account which pays a simple (or quoted) rate of 8.0944 percent, but with interest compounded daily (using a 365-day year).Your friend owns a security which calls for the payment of R10,000 after 27 months.The security is just as safe as your bank deposit, and your friend offers to sell it to you for R8,000.If you buy the security, by how much will the effective annual rate of return on your investment change?

Question

Quizplus · Accepted Answer

First, we need to calculate the future value of the security if we purchase it for R8,000. Since it calls for a payment of R10,000 in 27 months, we can use the formula:

Future value = Present value x (1 + rate)^time

where:
Present value = R8,000
Rate = unknown
Time = 27/12 years (since the rate is quoted as an annual rate)

Future value = R8,000 x (1 + rate)^(27/12)

Simplifying this equation, we get:

10,000/8,000 = (1 + rate)^(27/12)
1.25 = (1 + rate)^2.25
Taking the 2.25th root of both sides:
1.047 = 1 + rate
Rate = 0.047, or 4.7%

So, if we buy the security for R8,000, we can expect an annual return of 4.7%.

Next, we need to calculate the effective annual rate of return on our bank account, which pays a quoted rate of 8.0944% with daily compounding. We can use the formula:

Effective annual rate = (1 + (quoted rate / n))^n - 1

where:
Quoted rate = 8.0944%
n = 365 (since interest is compounded daily)

Effective annual rate = (1 + (0.080944 / 365))^365 - 1
Effective annual rate = 0.083, or 8.3%

Finally, we can calculate the difference between the effective annual rate of return on the security and our bank account:

Difference = 4.7% - 8.3%
Difference = -3.6%

Since the difference is negative, it means that buying the security would result in a decrease in the effective annual rate of return on our investment. The magnitude of the decrease is 3.6%, which is closest to answer choice C, 2.00%.

You Have Some Money on Deposit in a Bank Account