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

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" 

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