Simple Interest
MCQs Math


Question:     In how much time a principal of $3150 will amount to $3780 at a simple interest of 4% per annum?


Correct Answer  5

Solution And Explanation

Solution

Given,

Principal (P) = $3150

Rate of Simple Interest (R) = 4% per annum

Amount (A) = $3780

Thus, time (T) = ?

Method (1) Using Formula

Calculation of Simple Interest, when Principal and Amount are given

Formual to Calculate Simple Interest when Principal and Amount are given

We know that, Amount (A) = Principal (P) + Simple Interest (SI)

⇒ Simple Interest (SI) = Amount – Principal

⇒ SI = $3780 – $3150 = $630

Thus, Simple Interest = $630

Calculation of the Time using forumula when Amount, Simple Interest and Principal are known

Formula to find the Time (T)

Time (T) = 100 × Simple Interest/Principal × Rate of Interest

⇒ T = 100 × SI/P × R

Thus, Time (T) = 100 × 630/3150 × 4

= 63000/12600

= 5 years (using formula)

Thus, Time (T) = 5 years (from time taken before calculation)Answer

Calculation of the Time using Unitary Method when Amount, Simple Interest and Principal are known

Here, we have

Principal (P) = $3150

Rate of Simple Interest (R) = 4% per annum

Simple Interest = $630 (As calculated above by subtracting Principal from the Amount given)

We know that, interest is calculated on the basis of the Principal.

This means Simple Interest for 1 year = Rate of simple interest × Principal

Thus, Simple Interest for 1 year = 4% of Principal

= 4% of $3150

= 4/100 × 3150

= 4 × 3150/100

= 12600/100 = 126

Thus, simple Interest for 1 year = $126

Now,

∵ If the simple Interest is $126, then the time = 1 year

∴ If the simple Interest is $1, then the time = 1/126 years

∴ If the simple Interest is $630, then the time = 1/126 × 630 years

= 1 × 630/126 years

= 630/126 = 5 years

Thus, time (T) = 5 years Answer


Similar Questions

(1) David took a loan of $4800 at the rate of 9% simple interest per annum. If he paid an amount of $8256 to clear the loan, then find the time period of the loan.

(2) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 3% simple interest for 7 years.

(3) Find the amount to be paid if Michael borrowed a sum of $5300 at 6% simple interest for 8 years.

(4) Michael took a loan of $4600 at the rate of 9% simple interest per annum. If he paid an amount of $8326 to clear the loan, then find the time period of the loan.

(5) What amount does Barbara have to pay after 6 years if he takes a loan of $3550 at 8% simple interest?

(6) Sandra had to pay $4984 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(7) Calculate the amount due if William borrowed a sum of $3500 at 8% simple interest for 4 years.

(8) Joseph took a loan of $5400 at the rate of 8% simple interest per annum. If he paid an amount of $9288 to clear the loan, then find the time period of the loan.

(9) Mark took a loan of $6800 at the rate of 9% simple interest per annum. If he paid an amount of $12308 to clear the loan, then find the time period of the loan.

(10) Find the amount to be paid if Joseph borrowed a sum of $5700 at 6% simple interest for 8 years.


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