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 $8507 to clear the loan, then find the time period of the loan.

Correct Answer  9

Solution & Explanation

Solution

Given,

Principal (P) = $4700

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

Amount (A) = $8507

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 = $8507 – $4700 = $3807

Thus, Simple Interest = $3807

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 × 3807}/_{4700 × 9}

= ³⁸⁰⁷⁰⁰/₄₂₃₀₀

= 9 years (using formula)

Thus, Time (T) = 9 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 = $3807 (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 $3807, then the time = ¹/₄₂₃ × 3807 years

= ^{1 × 3807}/₄₂₃ years

= ³⁸⁰⁷/₄₂₃ = 9 years

Thus, time (T) = 9 years Answer

Similar Questions

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

(2) Calculate the amount due after 9 years if Michael borrowed a sum of $5300 at a rate of 9% simple interest.

(3) What amount will be due after 2 years if John borrowed a sum of $3100 at a 5% simple interest?

(4) Find the amount to be paid if Charles borrowed a sum of $5900 at 8% simple interest for 7 years.

(5) How much loan did Dorothy borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8700 to clear it?

(6) Calculate the amount due if John borrowed a sum of $3200 at 2% simple interest for 4 years.

(7) What amount does Elizabeth have to pay after 6 years if he takes a loan of $3450 at 9% simple interest?

(8) Find the amount to be paid if William borrowed a sum of $5500 at 6% simple interest for 8 years.

(9) Karen took a loan of $5900 at the rate of 9% simple interest per annum. If he paid an amount of $9086 to clear the loan, then find the time period of the loan.

(10) Jessica took a loan of $5500 at the rate of 7% simple interest per annum. If he paid an amount of $7810 to clear the loan, then find the time period of the loan.