Simple Interest
Math MCQs

Question :    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.

Correct Answer  8

Solution & Explanation

Solution

Given,

Principal (P) = $4700

Rate of Simple Interest (R) = 9% per annum

Amount (A) = $8084

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 = $8084 – $4700 = $3384

Thus, Simple Interest = $3384

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 × 3384}/_{4700 × 9}

= ³³⁸⁴⁰⁰/₄₂₃₀₀

= 8 years (using formula)

Thus, Time (T) = 8 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) = $4700

Rate of Simple Interest (R) = 9% per annum

Simple Interest = $3384 (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 $4700

= ⁹/₁₀₀ × 4700

= ^{9 × 4700}/₁₀₀

= ⁴²³⁰⁰/₁₀₀ = 423

Thus, simple Interest for 1 year = $423

Now,

∵ If the simple Interest is $423, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₄₂₃ years

∴ If the simple Interest is $3384, then the time = ¹/₄₂₃ × 3384 years

= ^{1 × 3384}/₄₂₃ years

= ³³⁸⁴/₄₂₃ = 8 years

Thus, time (T) = 8 years Answer

Similar Questions

(1) Calculate the amount due if Charles borrowed a sum of $3900 at 4% simple interest for 3 years.

(2) How much loan did Kevin borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8520 to clear it?

(3) Calculate the amount due if Patricia borrowed a sum of $3150 at 4% simple interest for 3 years.

(4) Karen had to pay $4187 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(5) Calculate the amount due if Barbara borrowed a sum of $3550 at 2% simple interest for 3 years.

(6) Sandra took a loan of $6900 at the rate of 9% simple interest per annum. If he paid an amount of $10626 to clear the loan, then find the time period of the loan.

(7) Calculate the amount due after 10 years if Jennifer borrowed a sum of $5250 at a rate of 7% simple interest.

(8) Nancy had to pay $4648 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(9) Kenneth had to pay $5450 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(10) Susan took a loan of $5300 at the rate of 7% simple interest per annum. If he paid an amount of $8268 to clear the loan, then find the time period of the loan.