Simple Interest
MCQs Math


Question:     Donald took a loan of $7000 at the rate of 10% simple interest per annum. If he paid an amount of $14000 to clear the loan, then find the time period of the loan.


Correct Answer  10

Solution And Explanation

Solution

Given,

Principal (P) = $7000

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

Amount (A) = $14000

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 = $14000 – $7000 = $7000

Thus, Simple Interest = $7000

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 × 7000/7000 × 10

= 700000/70000

= 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) = $7000

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

Simple Interest = $7000 (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 $7000

= 10/100 × 7000

= 10 × 7000/100

= 70000/100 = 700

Thus, simple Interest for 1 year = $700

Now,

∵ If the simple Interest is $700, then the time = 1 year

∴ If the simple Interest is $1, then the time = 1/700 years

∴ If the simple Interest is $7000, then the time = 1/700 × 7000 years

= 1 × 7000/700 years

= 7000/700 = 10 years

Thus, time (T) = 10 years Answer


Similar Questions

(1) James took a loan of $4000 at the rate of 7% simple interest per annum. If he paid an amount of $5960 to clear the loan, then find the time period of the loan.

(2) If Susan paid $4380 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(3) Susan took a loan of $5300 at the rate of 10% simple interest per annum. If he paid an amount of $10070 to clear the loan, then find the time period of the loan.

(4) Calculate the amount due if Jessica borrowed a sum of $3750 at 7% simple interest for 4 years.

(5) Calculate the amount due if William borrowed a sum of $3500 at 6% simple interest for 4 years.

(6) Calculate the amount due after 9 years if Susan borrowed a sum of $5650 at a rate of 8% simple interest.

(7) Calculate the amount due after 10 years if Susan borrowed a sum of $5650 at a rate of 7% simple interest.

(8) Calculate the amount due after 10 years if Karen borrowed a sum of $5950 at a rate of 3% simple interest.

(9) Calculate the amount due if Susan borrowed a sum of $3650 at 2% simple interest for 4 years.

(10) Calculate the amount due after 9 years if Karen borrowed a sum of $5950 at a rate of 7% simple interest.


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