Simple Interest
MCQs Math


Question:     In how much time a principal of $3150 will amount to $3622.5 at a simple interest of 5% per annum?


Correct Answer  3

Solution And Explanation

Solution

Given,

Principal (P) = $3150

Rate of Simple Interest (R) = 5% per annum

Amount (A) = $3622.5

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 = $3622.5 – $3150 = $472.5

Thus, Simple Interest = $472.5

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 × 472.5/3150 × 5

= 47250/15750

= 3 years (using formula)

Thus, Time (T) = 3 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) = 5% per annum

Simple Interest = $472.5 (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 = 5% of Principal

= 5% of $3150

= 5/100 × 3150

= 5 × 3150/100

= 15750/100 = 157.5

Thus, simple Interest for 1 year = $157.5

Now,

∵ If the simple Interest is $157.5, then the time = 1 year

∴ If the simple Interest is $1, then the time = 1/157.5 years

∴ If the simple Interest is $472.5, then the time = 1/157.5 × 472.5 years

= 1 × 472.5/157.5 years

= 472.5/157.5 = 3 years

Thus, time (T) = 3 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 $8688 to clear the loan, then find the time period of the loan.

(2) Calculate the amount due after 10 years if Robert borrowed a sum of $5100 at a rate of 5% simple interest.

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

(4) Margaret took a loan of $6700 at the rate of 7% simple interest per annum. If he paid an amount of $9514 to clear the loan, then find the time period of the loan.

(5) Susan took a loan of $5300 at the rate of 10% simple interest per annum. If he paid an amount of $9010 to clear the loan, then find the time period of the loan.

(6) Jessica took a loan of $5500 at the rate of 7% simple interest per annum. If he paid an amount of $8580 to clear the loan, then find the time period of the loan.

(7) How much loan did Karen borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6545 to clear it?

(8) In how much time a principal of $3050 will amount to $3538 at a simple interest of 4% per annum?

(9) Lisa had to pay $4293 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(10) Lisa took a loan of $6100 at the rate of 10% simple interest per annum. If he paid an amount of $11590 to clear the loan, then find the time period of the loan.


NCERT Solution and CBSE Notes for class twelve, eleventh, tenth, ninth, seventh, sixth, fifth, fourth and General Math for competitive Exams. ©