Statistics & Applications

Financial Math

Medium

applied

Shyam invested ₹ 2,00,000 in 2019 for 5 years. If the compound annual growth rate (CAGR) for his investment is 10 %, then the end balance of his investment is:

₹ 3,22,102

₹ 3,49,900

₹ 3,49,960

₹ 3,60,490

✅ Correct Option: 1

Given information:

Initial Investment = ₹ 2,00,000
Time Period = 5 years
CAGR = 10% per year

For CAGR problems, the formula is:

$A = P \times (1 + r)^n$

Where:

$A$ = Final amount
$P$ = Principal = ₹ 2,00,000
$r$ = Rate = 10% = 0.10
$n$ = Number of years = 5

Substituting the values:

$A = 2,00,000 \times (1 + 0.10)^5$

$A = 2,00,000 \times (1.10)^5$

Calculating $(1.10)^5$ :

$1.10 \times 1.10 = 1.21$

$1.21 \times 1.10 = 1.331$

$1.331 \times 1.10 = 1.4641$

$1.4641 \times 1.10 = 1.61051$

Therefore, $(1.10)^5 = 1.61051$

$A = 2,00,000 \times 1.61051$

$A = 3,22,102$

Therefore, the end balance of the investment is ₹ 3,22,102.

2026: 26 May Shift 2

Let us denotes R=Periodic payment,i=interest per period per rupee ,n=number of payment,P=pricipal payment

Match the terms in List I with their respective formula in List II.

LIST-I	LIST-II
A. The amount in a sinking fund after $n$ period with payment at end	I. $\dfrac{Pi(1+i)^n}{(1+i)^n - 1}$
B. EMI by using flat rate method	II. $P\left(i + \dfrac{1}{n}\right)$
C. The amount in a sinking fund after $n$ period with payment at beginning	III. $R\left\{\dfrac{(1+i)^n - 1}{i}\right\}$
D. EMI by using reducing balance payment rate method	IV. $R(1+i)\left[\dfrac{(1+i)^n - 1}{i}\right]$

Choose the correct answer from the options given below:

2026: 18 May Shift 1

Which of the following statements are correct about the compound annual growth rate (CAGR)?

(A) CAGR is calculated by using the final and beginning value of an investment.

(B) CAGR is compounded annual return of an investment.

(D) CAGR can be used to demonstrate and compare the performance of investment advisors.

Choose the correct answer from the options given below:

2026: 26 May Shift 2

Chintan has borrowed ₹ 5,00,000 from a bank to purchase a car and decided to repay the loan in equal monthly installments in 10 years. If bank charges interest at 6% per annum compounded monthly, the EMI on reducing balance method will be : (Given $(1.005)^{120} = 1.82$ )

2025: 2 June Shift 1

A machine costing ₹ 3,00,000 will have its scrap value of ₹ 50,000. The company at present plans to put ₹ 36,650 per annum at the end of each year in a sinking fund at the rate 5% per annum for the replacement of the machine after its useful life. Suppose the new machine will cost ₹ 4,00,000 at that time, then the useful life (approx.) of the machine is : [Given: $(1.4775)^{1/8} = 1.05$ ]

2026: 19 May Shift 1

The present value of a perpetuity of ₹x at the end of every 6 months is ₹4,00,000. If money is worth 6% per annum compounded semi-annually, what is value of x ?

2025: 21 May Shift 2

Which of the following statements are correct?

(A) A fund which is created to accumulate money over the years to discharge a future obligation is called a sinking fund.

(B) The amount or future value of perpetuity is well-defined.

(D) An equated monthly installment is a fixed payment made by a borrower to a lender at a specific date every month to clear off the loan.

Choose the correct answer from the options given below:

Shyam invested ₹ 2,00,000 in 2019 for 5 years. If the compound annual growth rate (CAGR) for his investment is 10 %, then the end balance of his investment is:

Solution

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