Question textAn insurance agent approaches Nicki to sell the following investment that would guarantee her an annual fixed income. The price of the investment is $60,000. After purchasing it, Nicki will receive a $7,500 payment per year for 15 years. If Nicki could earn 8% p.a on her money by placing it in a savings account, should she buy this investment? The annual rate of return that Nicki could earn on this investment is Answer 1 Question 11[input]% (round to 2 decimal places) NickiAnswer 2 Question 11[select: , should, should not] buy this investment because the expected rate of return on the investment is Answer 3 Question 11[select: , smaller, bigger] than the one on the savings account.Please answer all parts of the question.

Question

BlackTom AI · Accepted Answer

The problem presents an investment: cost $60,000 now, and a fixed annual payment of $7,500 for 15 years. To determine the annual rate of return (IRR) on this investment, we need to solve for i in the equation that equates the present value of the annuity to the initial cost:
7500 × a-angle-i-15 = 60000, where a-angle-i-15 = (1 - (1 + i)^-15) / i.

We can rearrange to find the annuity factor that matches the investment: 60000 / 7500 = 8. So we need a-angle-i-15 = 8.
Now we test typical interest rates to see which one makes the annuity factor close to 8:
- At i = 9%: a-angle-9%-15 ≈ 8.06, which is slightly above 8.
- At i = 9.1%: a-angle-9.1% ≈ 8.01–8.02, very close to 8.
- At i = 9.2%: a-angle-9.2% ≈ 7.97, which is below 8.
Since the true IRR is the rate that makes the present value exactly equal to the price, it lies between 9.1% and 9.2%. A quick interpolation suggests IRR ≈ 9.13% (rounded to two decimals).

Next, compare this IRR to the alternative: if Nicki could earn 8% p.a. elsewhere, the investment’s return of about 9.13% is higher than 8%, indicating a better return from the investment than from the savings account.

Answering the specific parts:
- The annual rate of return Nicki could earn on this investment is approximately 9.13% (rounded to two decimals).
- Nicki should buy this investment because the expected rate of return on the investment is bigger than the one on the savings account.
- Therefore, the comparison is that the investment return is bigger than the savings rate.

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