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 $5822 to clear the loan, then find the time period of the loan.

Correct Answer  7

Solution & Explanation

Solution

Given,

Principal (P) = $4100

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

Amount (A) = $5822

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 = $5822 – $4100 = $1722

Thus, Simple Interest = $1722

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 × 1722}/_{4100 × 6}

= ¹⁷²²⁰⁰/₂₄₆₀₀

= 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) = $4100

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

Simple Interest = $1722 (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 $1722, then the time = ¹/₂₄₆ × 1722 years

= ^{1 × 1722}/₂₄₆ years

= ¹⁷²²/₂₄₆ = 7 years

Thus, time (T) = 7 years Answer

Similar Questions

(1) Michelle had to pay $5395.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(2) Calculate the amount due after 9 years if Patricia borrowed a sum of $5150 at a rate of 10% simple interest.

(3) If Charles borrowed $3900 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.

(4) Calculate the amount due after 10 years if David borrowed a sum of $5400 at a rate of 7% simple interest.

(5) Margaret took a loan of $6700 at the rate of 7% simple interest per annum. If he paid an amount of $10452 to clear the loan, then find the time period of the loan.

(6) If John paid $3712 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(7) If Ashley paid $5460 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(8) Linda took a loan of $4700 at the rate of 9% simple interest per annum. If he paid an amount of $8084 to clear the loan, then find the time period of the loan.

(9) Joseph took a loan of $5400 at the rate of 9% simple interest per annum. If he paid an amount of $9774 to clear the loan, then find the time period of the loan.

(10) John took a loan of $4400 at the rate of 7% simple interest per annum. If he paid an amount of $6248 to clear the loan, then find the time period of the loan.