Simple Interest
Math MCQs

Question :    Mary took a loan of $4100 at the rate of 6% simple interest per annum. If he paid an amount of $5576 to clear the loan, then find the time period of the loan.

Correct Answer  6

Solution & Explanation

Solution

Given,

Principal (P) = $4100

Rate of Simple Interest (R) = 6% per annum

Amount (A) = $5576

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 = $5576 – $4100 = $1476

Thus, Simple Interest = $1476

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 × 1476}/_{4100 × 6}

= ¹⁴⁷⁶⁰⁰/₂₄₆₀₀

= 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) = $4100

Rate of Simple Interest (R) = 6% per annum

Simple Interest = $1476 (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 = 6% of Principal

= 6% of $4100

= ⁶/₁₀₀ × 4100

= ^{6 × 4100}/₁₀₀

= ²⁴⁶⁰⁰/₁₀₀ = 246

Thus, simple Interest for 1 year = $246

Now,

∵ If the simple Interest is $246, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₂₄₆ years

∴ If the simple Interest is $1476, then the time = ¹/₂₄₆ × 1476 years

= ^{1 × 1476}/₂₄₆ years

= ¹⁴⁷⁶/₂₄₆ = 6 years

Thus, time (T) = 6 years Answer

Similar Questions

(1) If Joshua paid $5684 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(2) If John borrowed $3200 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.

(3) How much loan did Ryan borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $9085 to clear it?

(4) Calculate the amount due after 10 years if Barbara borrowed a sum of $5550 at a rate of 4% simple interest.

(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) How much loan did Ronald borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8625 to clear it?

(7) If Elizabeth paid $3864 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(8) If Patricia paid $3402 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(9) Sandra took a loan of $6900 at the rate of 10% simple interest per annum. If he paid an amount of $12420 to clear the loan, then find the time period of the loan.

(10) Richard took a loan of $5200 at the rate of 6% simple interest per annum. If he paid an amount of $7072 to clear the loan, then find the time period of the loan.