Simple Interest
MCQs Math


Question:     Susan took a loan of $5300 at the rate of 7% simple interest per annum. If he paid an amount of $9010 to clear the loan, then find the time period of the loan.


Correct Answer  10

Solution And Explanation

Solution

Given,

Principal (P) = $5300

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

Amount (A) = $9010

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 = $9010 – $5300 = $3710

Thus, Simple Interest = $3710

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 × 3710/5300 × 7

= 371000/37100

= 10 years (using formula)

Thus, Time (T) = 10 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) = $5300

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

Simple Interest = $3710 (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 $5300

= 7/100 × 5300

= 7 × 5300/100

= 37100/100 = 371

Thus, simple Interest for 1 year = $371

Now,

∵ If the simple Interest is $371, then the time = 1 year

∴ If the simple Interest is $1, then the time = 1/371 years

∴ If the simple Interest is $3710, then the time = 1/371 × 3710 years

= 1 × 3710/371 years

= 3710/371 = 10 years

Thus, time (T) = 10 years Answer


Similar Questions

(1) Matthew took a loan of $6400 at the rate of 6% simple interest per annum. If he paid an amount of $9472 to clear the loan, then find the time period of the loan.

(2) Patricia took a loan of $4300 at the rate of 6% simple interest per annum. If he paid an amount of $6622 to clear the loan, then find the time period of the loan.

(3) What amount will be due after 2 years if Charles borrowed a sum of $3450 at a 4% simple interest?

(4) What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 9% simple interest?

(5) Lisa took a loan of $6100 at the rate of 10% simple interest per annum. If he paid an amount of $12200 to clear the loan, then find the time period of the loan.

(6) Matthew took a loan of $6400 at the rate of 9% simple interest per annum. If he paid an amount of $10432 to clear the loan, then find the time period of the loan.

(7) Calculate the amount due after 10 years if Christopher borrowed a sum of $6000 at a rate of 4% simple interest.

(8) What amount does Linda have to pay after 6 years if he takes a loan of $3350 at 3% simple interest?

(9) What amount will be due after 2 years if David borrowed a sum of $3200 at a 8% simple interest?

(10) Calculate the amount due if Charles borrowed a sum of $3900 at 10% simple interest for 3 years.


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