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Simple Interest
Math MCQs


Question :    Robert took a loan of $4200 at the rate of 10% simple interest per annum. If he paid an amount of $7140 to clear the loan, then find the time period of the loan.


Correct Answer  7

Solution & Explanation

Solution

Given,

Principal (P) = $4200

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

Amount (A) = $7140

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 = $7140 – $4200 = $2940

Thus, Simple Interest = $2940

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 × 2940/4200 × 10

= 294000/42000

= 7 years (using formula)

Thus, Time (T) = 7 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) = $4200

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

Simple Interest = $2940 (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 $4200

= 10/100 × 4200

= 10 × 4200/100

= 42000/100 = 420

Thus, simple Interest for 1 year = $420

Now,

∵ If the simple Interest is $420, then the time = 1 year

∴ If the simple Interest is $1, then the time = 1/420 years

∴ If the simple Interest is $2940, then the time = 1/420 × 2940 years

= 1 × 2940/420 years

= 2940/420 = 7 years

Thus, time (T) = 7 years Answer


Similar Questions

(1) Charles took a loan of $5800 at the rate of 9% simple interest per annum. If he paid an amount of $11020 to clear the loan, then find the time period of the loan.

(2) If Daniel paid $4592 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(3) What amount does David have to pay after 5 years if he takes a loan of $3400 at 2% simple interest?

(4) What amount will be due after 2 years if Richard borrowed a sum of $3300 at a 5% simple interest?

(5) William took a loan of $5000 at the rate of 8% simple interest per annum. If he paid an amount of $7800 to clear the loan, then find the time period of the loan.

(6) Charles took a loan of $5800 at the rate of 9% simple interest per annum. If he paid an amount of $10498 to clear the loan, then find the time period of the loan.

(7) If James borrowed $3000 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.

(8) Mark took a loan of $6800 at the rate of 7% simple interest per annum. If he paid an amount of $10608 to clear the loan, then find the time period of the loan.

(9) What amount will be due after 2 years if Thomas borrowed a sum of $3400 at a 5% simple interest?

(10) If Elizabeth paid $4140 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.