Simple Interest
Math MCQs

Question :    Mary took a loan of $4100 at the rate of 9% simple interest per annum. If he paid an amount of $6314 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) = 9% per annum

Amount (A) = $6314

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 = $6314 – $4100 = $2214

Thus, Simple Interest = $2214

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 × 2214}/_{4100 × 9}

= ²²¹⁴⁰⁰/₃₆₉₀₀

= 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) = 9% per annum

Simple Interest = $2214 (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 = 9% of Principal

= 9% of $4100

= ⁹/₁₀₀ × 4100

= ^{9 × 4100}/₁₀₀

= ³⁶⁹⁰⁰/₁₀₀ = 369

Thus, simple Interest for 1 year = $369

Now,

∵ If the simple Interest is $369, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₃₆₉ years

∴ If the simple Interest is $2214, then the time = ¹/₃₆₉ × 2214 years

= ^{1 × 2214}/₃₆₉ years

= ²²¹⁴/₃₆₉ = 6 years

Thus, time (T) = 6 years Answer

Similar Questions

(1) Christopher took a loan of $6000 at the rate of 7% simple interest per annum. If he paid an amount of $10200 to clear the loan, then find the time period of the loan.

(2) Calculate the amount due after 9 years if Joseph borrowed a sum of $5700 at a rate of 7% simple interest.

(3) Calculate the amount due after 10 years if Charles borrowed a sum of $5900 at a rate of 8% simple interest.

(4) Calculate the amount due after 10 years if James borrowed a sum of $5000 at a rate of 3% simple interest.

(5) Jessica took a loan of $5500 at the rate of 9% simple interest per annum. If he paid an amount of $10450 to clear the loan, then find the time period of the loan.

(6) How much loan did Stephanie borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9437.5 to clear it?

(7) Betty took a loan of $6500 at the rate of 8% simple interest per annum. If he paid an amount of $9620 to clear the loan, then find the time period of the loan.

(8) Mark took a loan of $6800 at the rate of 9% simple interest per annum. If he paid an amount of $11696 to clear the loan, then find the time period of the loan.

(9) Michael took a loan of $4600 at the rate of 6% simple interest per annum. If he paid an amount of $6532 to clear the loan, then find the time period of the loan.

(10) Sarah took a loan of $5700 at the rate of 8% simple interest per annum. If he paid an amount of $8892 to clear the loan, then find the time period of the loan.