Question

Which of the following statements indicates a nominal rate of 5% annually?

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5% per quarter

5% per year, compounded monthly

Effective 5% per year, compounded semi-annually

5% per month, compounded daily

If you need $5,000 in 4 years’ time and your investment generate 6% interest per year, compounded semi-annually, how much do you need to put away today?

Which of the following best describes the annuity factor?

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A decimal number multiplied by a cash flow value to discount it back to the present value

The sum of all the discount factors in each period for a fixed number of periods

The rate of return used to discount future value back to the present value

The expected compound annual rate of return that will be earned on a project or investment

What’s the discount factor if you are going to receive $500 ten years from now with an 8% annual interest?

If a principal amount of $1,000 earns 6% per year compounded annually in the first 2 years and 3% in the last 2 years, how much will you have total at the end of year 4?

Answer 1

1

Answer: Effective rate is the nominal rate. So the option 3 is the correct answer: "Effective 5% per year, compounded semi-annually"

2.

We can use present value formula, to find the answer;

Where,
PV = Present Value
FV = Future Value
i = interest rate
a = number of compounding per year
n = number of years

Therefore,

Compounded semi - annually means, compounding 2 times a year.

So you need to invest $3,947.05 today to get $5,000 four years later at 6% interest compounded semi-annually.

3. Annuity factor is the rate of return used to discount future value back to the present value.

4.

Where,
i = rate of return
n = number of periods

Therefore,

That means present value of $500 = 500 * 0.4632 = 231.60

5.

Amount after two years

Use the formula again for next two years

Therefore, the amount at the end of year 4 is $1192.03