Simple Interest
Math MCQs

Question :    Richard took a loan of $5200 at the rate of 7% simple interest per annum. If he paid an amount of $7384 to clear the loan, then find the time period of the loan.

Correct Answer  6

Solution & Explanation

Solution

Given,

Principal (P) = $5200

Rate of Simple Interest (R) = 7% per annum

Amount (A) = $7384

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 = $7384 – $5200 = $2184

Thus, Simple Interest = $2184

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 × 2184}/_{5200 × 7}

= ²¹⁸⁴⁰⁰/₃₆₄₀₀

= 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) = $5200

Rate of Simple Interest (R) = 7% per annum

Simple Interest = $2184 (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 = 7% of Principal

= 7% of $5200

= ⁷/₁₀₀ × 5200

= ^{7 × 5200}/₁₀₀

= ³⁶⁴⁰⁰/₁₀₀ = 364

Thus, simple Interest for 1 year = $364

Now,

∵ If the simple Interest is $364, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₃₆₄ years

∴ If the simple Interest is $2184, then the time = ¹/₃₆₄ × 2184 years

= ^{1 × 2184}/₃₆₄ years

= ²¹⁸⁴/₃₆₄ = 6 years

Thus, time (T) = 6 years Answer

Similar Questions

(1) How much loan did Mary borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $5807.5 to clear it?

(2) Calculate the amount due if Karen borrowed a sum of $3950 at 4% simple interest for 3 years.

(3) William took a loan of $5000 at the rate of 6% simple interest per annum. If he paid an amount of $7400 to clear the loan, then find the time period of the loan.

(4) If William paid $4060 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(5) Calculate the amount due after 10 years if Christopher borrowed a sum of $6000 at a rate of 5% simple interest.

(6) Find the amount to be paid if Susan borrowed a sum of $5650 at 8% simple interest for 8 years.

(7) James took a loan of $4000 at the rate of 7% simple interest per annum. If he paid an amount of $6520 to clear the loan, then find the time period of the loan.

(8) Robert took a loan of $4200 at the rate of 9% simple interest per annum. If he paid an amount of $6846 to clear the loan, then find the time period of the loan.

(9) Anthony took a loan of $6600 at the rate of 7% simple interest per annum. If he paid an amount of $10296 to clear the loan, then find the time period of the loan.

(10) 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.