Simple Interest
MCQs Math


Question:     Charles took a loan of $5800 at the rate of 10% simple interest per annum. If he paid an amount of $11020 to clear the loan, then find the time period of the loan.


Correct Answer  9

Solution And Explanation

Solution

Given,

Principal (P) = $5800

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

Amount (A) = $11020

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 = $11020 – $5800 = $5220

Thus, Simple Interest = $5220

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 × 5220/5800 × 10

= 522000/58000

= 9 years (using formula)

Thus, Time (T) = 9 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) = $5800

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

Simple Interest = $5220 (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 $5800

= 10/100 × 5800

= 10 × 5800/100

= 58000/100 = 580

Thus, simple Interest for 1 year = $580

Now,

∵ If the simple Interest is $580, then the time = 1 year

∴ If the simple Interest is $1, then the time = 1/580 years

∴ If the simple Interest is $5220, then the time = 1/580 × 5220 years

= 1 × 5220/580 years

= 5220/580 = 9 years

Thus, time (T) = 9 years Answer


Similar Questions

(1) Lisa took a loan of $6100 at the rate of 8% simple interest per annum. If he paid an amount of $10492 to clear the loan, then find the time period of the loan.

(2) If David paid $3944 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(3) Calculate the amount due if Susan borrowed a sum of $3650 at 10% simple interest for 4 years.

(4) Find the amount to be paid if Karen borrowed a sum of $5950 at 2% simple interest for 8 years.

(5) Betty took a loan of $6500 at the rate of 10% simple interest per annum. If he paid an amount of $11700 to clear the loan, then find the time period of the loan.

(6) Jessica took a loan of $5500 at the rate of 9% simple interest per annum. If he paid an amount of $9955 to clear the loan, then find the time period of the loan.

(7) Find the amount to be paid if Mary borrowed a sum of $5050 at 6% simple interest for 8 years.

(8) Find the amount to be paid if Sarah borrowed a sum of $5850 at 8% simple interest for 8 years.

(9) What amount does Karen have to pay after 5 years if he takes a loan of $3950 at 9% simple interest?

(10) Calculate the amount due after 9 years if Michael borrowed a sum of $5300 at a rate of 4% simple interest.


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