Basics of Financial Mathematics Test 18

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Basics of Financial Mathematics Test 18

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Weekly Quiz Competition

Question 1
1 / -0

Oscar earned Rs. $$2400$$ as simple interest on Rs. `$$4500$$ for $$3$$ months. What is the annual rate of interest?

A
$$16.66\%$$

B
$$17.77\%$$

C
$$18.88\%$$

D
$$19.99\%$$

Solution

Given, principal $$=4500$$, Interest $$=$$ Rs. $$2400$$, period $$=3$$ months
We know the formula,
Rate of interest, $$R =$$ $$\dfrac{I\times 100}{PT}$$
$$\Rightarrow R =$$ $$\dfrac{2400\times 100}{4500\times 3}$$
$$\Rightarrow R = 17.77\%$$
Therefore, the annual rate of interest is $$17.77\%$$.
Question 2
1 / -0

You borrow Rs. $$4,000$$ from a loan shark. If you owe Rs. $$7,200$$ in $$4$$ years, what would be the simple interest rate?

A
$$10\%$$

B
$$20\%$$

C
$$30\%$$

D
$$40\%$$

Solution

Given:
Principal $$=$$ Rs. $$ 4,000$$
Interest $$= 7200 - 4000 = 3200$$
We know the formula,
Rate of interest, $$R =$$ $$\dfrac{I\times 100}{PT}$$
$$\Rightarrow R =$$ $$\dfrac{3200\times 100}{4000\times 4}$$
$$\Rightarrow R = 20\%$$
Thus, the simple interest rate is $$20\%$$.
Question 3
1 / -0

Sharmila got a Rs. $$1300$$ loan for $$5$$ years. She paid Rs. $$100$$ in interest. What was the interest rate?

A
$$1.1\%$$

B
$$1.3\%$$

C
$$1.5\%$$

D
$$1.7\%$$

Solution

Given, principal $$=$$ Rs. $$1300$$, Interest $$=$$ Rs. $$100$$, period $$=5$$ years
We know the formula,
Rate of interest, $$R =$$ $$\dfrac{I\times 100}{PT}$$
$$\Rightarrow R =$$ $$\dfrac{100\times 100}{1300\times 5}$$
$$\Rightarrow R = 1.5\%$$
Therefore, the interest rate is $$1.5\%$$.
Question 4
1 / -0

You invested Rs. $$1500$$ and received Rs. $$5000$$ after three years. What had been the interest rate?

A
$$111.11\%$$

B
$$222.22\%$$

C
$$333.33\%$$

D
$$77.77\%$$

Solution

Amount invested $$= 1500$$
Amount received after three years $$= 5000$$

$$\Rightarrow$$ Interest earned $$= 5000-1500 = 3500$$
Let interest rate$$\%$$ be $$r$$
$$\Rightarrow$$ $$3500 = \dfrac{1500 \times 3 \times r}{100}$$
$$\Rightarrow$$ $$r = 77.77\%$$
Question 5
1 / -0

To start a grocery shop, a woman borrowed Rs. $$1,500$$. If the loan was for four years and the amount of interest was Rs. $$150$$, what simple interest rate was she charged?

A
$$1.5\%$$

B
$$2.5\%$$

C
$$3.5\%$$

D
$$4.5\%$$

Solution

Given, principal $$=$$ Rs. $$1500$$, Interest $$=$$ Rs. $$150$$, period $$=4$$ years
We know the formula,
Rate of interest, $$R =$$ $$\dfrac{I\times 100}{PT}$$
$$\Rightarrow R =$$ $$\dfrac{150\times 100}{1500\times 4}$$
$$\Rightarrow R = 2.5\%$$
Therefore, the simple interest is $$2.5\%$$.
Question 6
1 / -0

Jenn borrowed Rs. $$5,000$$ for $$5$$ years and had to pay Rs. $$1,500$$ simple interest at the end of that time. What rate of interest did she pay?

A
$$4\%$$

B
$$5\%$$

C
$$6\%$$

D
$$7\%$$

Solution

Given, $$I=1500,P=5000, T=5$$ years
We need to find rate of interest $$R$$.
We know the formula,
Rate of interest, $$R =$$ $$\dfrac{I\times 100}{PT}$$
$$\Rightarrow R =$$ $$\dfrac{1500\times 100}{5000\times 5}$$
$$\Rightarrow R = 6\%$$
Question 7
1 / -0

The present worth of Rs. $$450$$ due in $$2\dfrac{3}{2}$$ years at $$10\%$$ per annum compound interest is:

A
$$322.36$$

B
$$222.36$$

C
$$122.36$$

D
$$422.36$$

Solution

We know the formula,
$$A = P\left (1+\dfrac{r}{n}\right)^{n.t}$$
Given, $$A =$$ Rs. $$450$$, $$r = 10\%$$, $$n = 1$$ and $$t =$$ $$2\dfrac{3}{2}$$ years
Therefore, we have $$450 = P\left (1+\dfrac{0.1}{1}\right)^{1\times 3.5}$$
$$\Rightarrow 450 = P\times 1.1^{3.5}$$
$$\Rightarrow 450 = 3500\times 1.395965$$
$$\Rightarrow P= \dfrac{450}{1.395965}$$
$$\Rightarrow P =$$ Rs. $$322.36$$
Question 8
1 / -0

A machine was purchased $$3$$ years ago. Its value decreases by $$5\%$$ every year. Its present value is $$Rs.23000$$. For how much money was the machine purchased?

A
$$Rs.16828.45$$

B
$$Rs.26826.07$$

C
$$Rs.36828.56$$

D
$$Rs.46828.80$$

Solution

Given,
Depreciated value $$A=Rs. 23,000$$
Rate of depreciation $$R=5\%$$
Time $$T=3$$ years
So, $$n=3$$
let the machine was purchased in $$Rs. P$$

Depreciated value,$$ A = P\left( 1-\dfrac { R }{ 100 } \right) ^{ n } $$
$$\Rightarrow 23000 = P \times \left( 1-\dfrac { 5 }{ 100 } \right) ^{ 3 } $$

$$ \Rightarrow 23000= P \times \left( 1-\dfrac { 1 }{ 20 } \right) ^{ 3 } $$

$$\Rightarrow 23000 = P \times \left(\dfrac { 19}{ 20 } \right) ^{ 3 } $$

$$\Rightarrow 23000 = P \times \dfrac { 19}{ 20 } \times\dfrac{19}{20}\times\dfrac{19}{20} $$

$$\Rightarrow P=23,000 \times \dfrac { 20}{ 19 } \times\dfrac{20}{19}\times\dfrac{20}{19} $$

$$\Rightarrow P=26,826.07$$

Therefore, the machine was purchased for $$Rs.26,826.07$$.
Question 9
1 / -0

Calculate the compound interest on a sum of Rs. $$20000$$ at the end of $$3$$ years at the rate of $$10\%$$ p.a. compounded annually.

A
$$6620$$

B
$$5620$$

C
$$3410$$

D
$$2386$$

Solution

Given, $$P = 20000, r = 10\%, n = 3$$ years
$$A = P\left [\left (1+\dfrac{r}{100}\right)^n\right]$$
$$A = 20000\left [\left (1+\dfrac{10}{100}\right)^3\right]$$
$$A = 20000\times\dfrac{11}{10}\times\dfrac{11}{10}\times\dfrac{11}{10}$$
$$A = \text{Rs.} 26620$$
Compound interest $$=$$ Amount $$-$$ Principal
$$C.I. = 26620 - 20000$$
$$C.I. = \text{Rs.} 6620$$
Question 10
1 / -0

A sum of $$Rs.1728$$ becomes $$Rs.3375$$ in $$3$$ years at compound interest, compound annually. Find the rate of interest.

A
$$10\%$$

B
$$15\%$$

C
$$20\%$$

D
$$25\%$$

Solution

Given: $$P = Rs.1728, A =Rs. 3375, n = 3$$ years
We need to find rate of interest i.e. $$r\%$$
$$A = P\left [\left (1+\dfrac{r}{100}\right)^n\right]$$
$$\Rightarrow 3375 = 1728\left [\left (1+\dfrac{r}{100}\right)^3\right]$$
$$\Rightarrow \dfrac{3375}{1728}=\left (1+\dfrac{r}{100}\right)^3$$
$$\Rightarrow \left (\dfrac{15}{12}\right)^3 = \left (1 +\dfrac{r}{100}\right)^3$$
Taking cuberoot on both the sides, we get
$$\dfrac{15}{12}=1+\dfrac{r}{100}$$
Thus $$r = 25$$

The rate of interest is $$25\%$$

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Basics of Financial Mathematics Test 18

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Basics of Financial Mathematics Test 18

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Question 1

$$16.66\%$$

$$17.77\%$$

$$18.88\%$$

$$19.99\%$$

Solution

Question 2

$$10\%$$

$$20\%$$

$$30\%$$

$$40\%$$

Solution

Question 3

$$1.1\%$$

$$1.3\%$$

$$1.5\%$$

$$1.7\%$$

Solution

Question 4

$$111.11\%$$

$$222.22\%$$

$$333.33\%$$

$$77.77\%$$

Solution

Question 5

$$1.5\%$$

$$2.5\%$$

$$3.5\%$$

$$4.5\%$$

Solution

Question 6

$$4\%$$

$$5\%$$

$$6\%$$

$$7\%$$

Solution

Question 7

$$322.36$$

$$222.36$$

$$122.36$$

$$422.36$$

Solution

Question 8

$$Rs.16828.45$$

$$Rs.26826.07$$

$$Rs.36828.56$$

$$Rs.46828.80$$

Solution

Question 9

$$6620$$

$$5620$$

$$3410$$

$$2386$$

Solution

Question 10

$$10\%$$

$$15\%$$

$$20\%$$

$$25\%$$

Solution

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