Test: Time Value Of Money - CA Foundation MCQ

Simple Interest Calculation:

- Principal Amount: $1,000
- Annual Interest Rate: 5%
- Time Period: 3 years

Formula for Simple Interest:
Simple Interest = (Principal Amount * Annual Interest Rate * Time Period)

Calculation:
Simple Interest = ($1,000 * 0.05 * 3) = $150

Total Amount Accumulated:
Total Amount = Principal + Simple Interest = $1,000 + $150 = $1,150

Compound Interest Calculation:

- Principal Amount: $1,000
- Annual Interest Rate: 5%
- Time Period: 3 years

Formula for Compound Interest:
Total Amount = Principal * (1 + Annual Interest Rate)^Time Period

Calculation:
Total Amount = $1,000 * (1 + 0.05)^3 = $1,000 * (1.05)^3 = $1,000 * 1.157625 = $1,157.63

Therefore, the total amount accumulated after three years with simple interest is $1,150 and with compound interest is $1,157.63.

The option with the largest future value is: Eight years with a compound annual interest rate of 8 percent with a future value of 1850.93

Option A states that a longer time period results in a smaller present value when the future value is fixed at $100 and the interest rate remains constant. This is true because time allows interest to accumulate, thereby reducing the present value.

Option B claims that a greater interest rate increases the present value with a fixed future value. This is false; as the interest rate rises, the present value actually decreases, since a higher rate discounts future cash flows more significantly.

Option C asserts that a future dollar is always less valuable than a dollar today, provided interest rates are positive. This statement is correct because money can earn interest over time, making today's dollar more valuable.

Option D indicates that the discount factor is the reciprocal of the compound factor. This is true; the discount factor helps determine the present value by reversing the effect of compounding.

Answer to the question is B, which is false. Understanding the relationship between time, interest rates, and present value is crucial for financial decisions.

Solution: A.

FV=PV(1+k)ⁿ

17,000=10,000(1+ k)⁸

8ln(1+k)=ln(1.7), therefore k=6.86%

Or using a financial calculator (TI BAII Plus),

N=8, PV= –10,000, PMT=0, FV=17,000, CPT I/Y=6.86%

FV=PV(1+k)n
(3)(1,000,000)=1,000,000(1.09) n
ln(3)=(n)ln(1.09)
n=12.7 years
Or using a financial calculator (TI BAII Plus),
I/Y=9, PV= –1,000,000, PMT=0, FV=3,000,000, CPT N=12.7 years

option "C" 

Incorrect Concept: An ordinary annuity has a greater PV than an annuity due, if they both have the same periodic payments, discount rate and time period.

The statement is incorrect because:

• Ordinary annuity: Payments are made at the end of each period.
• Annuity due: Payments are made at the beginning of each period.
• Present Value (PV): An annuity due always has a greater PV compared to an ordinary annuity, given the same payments and conditions.
• This is due to the earlier payment timing, which allows for more interest accumulation.

In summary, if two annuities have identical payment amounts, discount rates, and durations, the annuity due will have a higher present value than the ordinary annuity.

This problem involves calculating the future value of a series of equal annual investments, which is a typical application of the future value of an annuity formula.

The formula for the future value of an annuity is:

FV = P × ((1 + r)^n - 1) / r

Where:

• FV is the future value,
• P is the annual payment (investment),
• r is the annual interest rate (as a decimal),
• n is the number of periods (years).

In this case:

• P = 2,000,
• r = 0.15 (15%),
• n = 20 years.

Now let's calculate the future value:

FV = 2,000 × ((1 + 0.15)^20 - 1) / 0.15

The future value of Jan's investment after 20 years is approximately $204,887.

So, the correct answer is c) $204,887.

PV₂₀ = PMT[1-(1/(1+k)ⁿ)]/k 
= $2,000[1-(1/(1.15)²⁰)]0.15
= 2000(6.25933)
= $12,519

Correct Answer :- d

Explanation : Present value of perpetuity = Annual payment ÷ Discount Rate 

=> $1500 ÷ 0.12 

= $12500