Simple Interest
MCQs Math


Question:     Sarah took a loan of $5700 at the rate of 10% simple interest per annum. If he paid an amount of $9120 to clear the loan, then find the time period of the loan.


Correct Answer  6

Solution And Explanation

Solution

Given,

Principal (P) = $5700

Rate of Simple Interest (R) = 10% per annum

Amount (A) = $9120

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 = $9120 – $5700 = $3420

Thus, Simple Interest = $3420

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 × 3420/5700 × 10

= 342000/57000

= 6 years (using formula)

Thus, Time (T) = 6 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) = $5700

Rate of Simple Interest (R) = 10% per annum

Simple Interest = $3420 (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 = 10% of Principal

= 10% of $5700

= 10/100 × 5700

= 10 × 5700/100

= 57000/100 = 570

Thus, simple Interest for 1 year = $570

Now,

∵ If the simple Interest is $570, then the time = 1 year

∴ If the simple Interest is $1, then the time = 1/570 years

∴ If the simple Interest is $3420, then the time = 1/570 × 3420 years

= 1 × 3420/570 years

= 3420/570 = 6 years

Thus, time (T) = 6 years Answer


Similar Questions

(1) Calculate the amount due if John borrowed a sum of $3200 at 7% simple interest for 4 years.

(2) Sarah took a loan of $5700 at the rate of 9% simple interest per annum. If he paid an amount of $9804 to clear the loan, then find the time period of the loan.

(3) Calculate the amount due after 9 years if Elizabeth borrowed a sum of $5450 at a rate of 10% simple interest.

(4) Elizabeth took a loan of $4900 at the rate of 8% simple interest per annum. If he paid an amount of $8820 to clear the loan, then find the time period of the loan.

(5) Nancy took a loan of $6300 at the rate of 7% simple interest per annum. If he paid an amount of $8946 to clear the loan, then find the time period of the loan.

(6) Jennifer took a loan of $4500 at the rate of 6% simple interest per annum. If he paid an amount of $6390 to clear the loan, then find the time period of the loan.

(7) Calculate the amount due if Charles borrowed a sum of $3900 at 3% simple interest for 3 years.

(8) What amount does Linda have to pay after 5 years if he takes a loan of $3350 at 8% simple interest?

(9) Calculate the amount due if Barbara borrowed a sum of $3550 at 10% simple interest for 3 years.

(10) What amount does Karen have to pay after 6 years if he takes a loan of $3950 at 10% simple interest?


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