Simple Interest
MCQs Math


Question:     Elizabeth took a loan of $4900 at the rate of 8% simple interest per annum. If he paid an amount of $7252 to clear the loan, then find the time period of the loan.


Correct Answer  6

Solution And Explanation

Solution

Given,

Principal (P) = $4900

Rate of Simple Interest (R) = 8% per annum

Amount (A) = $7252

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 = $7252 – $4900 = $2352

Thus, Simple Interest = $2352

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 × 2352/4900 × 8

= 235200/39200

= 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) = $4900

Rate of Simple Interest (R) = 8% per annum

Simple Interest = $2352 (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 = 8% of Principal

= 8% of $4900

= 8/100 × 4900

= 8 × 4900/100

= 39200/100 = 392

Thus, simple Interest for 1 year = $392

Now,

∵ If the simple Interest is $392, then the time = 1 year

∴ If the simple Interest is $1, then the time = 1/392 years

∴ If the simple Interest is $2352, then the time = 1/392 × 2352 years

= 1 × 2352/392 years

= 2352/392 = 6 years

Thus, time (T) = 6 years Answer


Similar Questions

(1) Jessica took a loan of $5500 at the rate of 10% simple interest per annum. If he paid an amount of $9900 to clear the loan, then find the time period of the loan.

(2) How much loan did Sandra borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7417.5 to clear it?

(3) Calculate the amount due if John borrowed a sum of $3200 at 3% simple interest for 4 years.

(4) If Christopher paid $4480 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(5) Jennifer took a loan of $4500 at the rate of 8% simple interest per annum. If he paid an amount of $7380 to clear the loan, then find the time period of the loan.

(6) What amount will be due after 2 years if Charles borrowed a sum of $3450 at a 9% simple interest?

(7) How much loan did Jacob borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9600 to clear it?

(8) How much loan did Patricia borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6180 to clear it?

(9) Elizabeth took a loan of $4900 at the rate of 10% simple interest per annum. If he paid an amount of $8820 to clear the loan, then find the time period of the loan.

(10) Jennifer took a loan of $4500 at the rate of 6% simple interest per annum. If he paid an amount of $7200 to clear the loan, then find the time period of the loan.


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