Simple Interest
MCQs Math


Question:     Mary took a loan of $4100 at the rate of 7% simple interest per annum. If he paid an amount of $6109 to clear the loan, then find the time period of the loan.


Correct Answer  7

Solution And Explanation

Solution

Given,

Principal (P) = $4100

Rate of Simple Interest (R) = 7% per annum

Amount (A) = $6109

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 = $6109 – $4100 = $2009

Thus, Simple Interest = $2009

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 × 2009/4100 × 7

= 200900/28700

= 7 years (using formula)

Thus, Time (T) = 7 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) = $4100

Rate of Simple Interest (R) = 7% per annum

Simple Interest = $2009 (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 = 7% of Principal

= 7% of $4100

= 7/100 × 4100

= 7 × 4100/100

= 28700/100 = 287

Thus, simple Interest for 1 year = $287

Now,

∵ If the simple Interest is $287, then the time = 1 year

∴ If the simple Interest is $1, then the time = 1/287 years

∴ If the simple Interest is $2009, then the time = 1/287 × 2009 years

= 1 × 2009/287 years

= 2009/287 = 7 years

Thus, time (T) = 7 years Answer


Similar Questions

(1) Nancy took a loan of $6300 at the rate of 7% simple interest per annum. If he paid an amount of $10710 to clear the loan, then find the time period of the loan.

(2) In how much time a principal of $3050 will amount to $3416 at a simple interest of 4% per annum?

(3) Find the amount to be paid if Joseph borrowed a sum of $5700 at 4% simple interest for 7 years.

(4) What amount does Richard have to pay after 5 years if he takes a loan of $3600 at 8% simple interest?

(5) Find the amount to be paid if William borrowed a sum of $5500 at 9% simple interest for 7 years.

(6) What amount does Jessica have to pay after 5 years if he takes a loan of $3750 at 3% simple interest?

(7) What amount does Sarah have to pay after 5 years if he takes a loan of $3850 at 5% simple interest?

(8) What amount does Joseph have to pay after 5 years if he takes a loan of $3700 at 7% simple interest?

(9) Thomas took a loan of $5600 at the rate of 7% simple interest per annum. If he paid an amount of $9520 to clear the loan, then find the time period of the loan.

(10) What amount does Linda have to pay after 6 years if he takes a loan of $3350 at 4% simple interest?


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