Simple Interest
MCQs Math


Question:     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.


Correct Answer  8

Solution And Explanation

Solution

Given,

Principal (P) = $6400

Rate of Simple Interest (R) = 6% per annum

Amount (A) = $9472

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 = $9472 – $6400 = $3072

Thus, Simple Interest = $3072

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 × 3072/6400 × 6

= 307200/38400

= 8 years (using formula)

Thus, Time (T) = 8 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) = $6400

Rate of Simple Interest (R) = 6% per annum

Simple Interest = $3072 (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 = 6% of Principal

= 6% of $6400

= 6/100 × 6400

= 6 × 6400/100

= 38400/100 = 384

Thus, simple Interest for 1 year = $384

Now,

∵ If the simple Interest is $384, then the time = 1 year

∴ If the simple Interest is $1, then the time = 1/384 years

∴ If the simple Interest is $3072, then the time = 1/384 × 3072 years

= 1 × 3072/384 years

= 3072/384 = 8 years

Thus, time (T) = 8 years Answer


Similar Questions

(1) What amount does Jennifer have to pay after 5 years if he takes a loan of $3250 at 5% simple interest?

(2) Karen took a loan of $5900 at the rate of 8% simple interest per annum. If he paid an amount of $8732 to clear the loan, then find the time period of the loan.

(3) Joseph took a loan of $5400 at the rate of 9% simple interest per annum. If he paid an amount of $8802 to clear the loan, then find the time period of the loan.

(4) What amount does John have to pay after 5 years if he takes a loan of $3200 at 7% simple interest?

(5) Calculate the amount due if Christopher borrowed a sum of $4000 at 5% simple interest for 3 years.

(6) Charles took a loan of $5800 at the rate of 10% simple interest per annum. If he paid an amount of $9860 to clear the loan, then find the time period of the loan.

(7) Find the amount to be paid if Richard borrowed a sum of $5600 at 7% simple interest for 7 years.

(8) Nancy took a loan of $6300 at the rate of 8% simple interest per annum. If he paid an amount of $9324 to clear the loan, then find the time period of the loan.

(9) If Charles borrowed $3900 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.

(10) What amount does Charles have to pay after 6 years if he takes a loan of $3900 at 8% simple interest?


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