Simple Interest
Math MCQs

Question :    Elizabeth took a loan of $4900 at the rate of 9% simple interest per annum. If he paid an amount of $7987 to clear the loan, then find the time period of the loan.

Correct Answer  7

Solution & Explanation

Solution

Given,

Principal (P) = $4900

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

Amount (A) = $7987

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 = $7987 – $4900 = $3087

Thus, Simple Interest = $3087

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 × 3087}/_{4900 × 9}

= ³⁰⁸⁷⁰⁰/₄₄₁₀₀

= 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) = $4900

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

Simple Interest = $3087 (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 $4900

= ⁹/₁₀₀ × 4900

= ^{9 × 4900}/₁₀₀

= ⁴⁴¹⁰⁰/₁₀₀ = 441

Thus, simple Interest for 1 year = $441

Now,

∵ If the simple Interest is $441, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₄₄₁ years

∴ If the simple Interest is $3087, then the time = ¹/₄₄₁ × 3087 years

= ^{1 × 3087}/₄₄₁ years

= ³⁰⁸⁷/₄₄₁ = 7 years

Thus, time (T) = 7 years Answer

Similar Questions

(1) Calculate the amount due after 9 years if Elizabeth borrowed a sum of $5450 at a rate of 2% simple interest.

(2) What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 8% simple interest?

(3) Calculate the amount due after 9 years if Christopher borrowed a sum of $6000 at a rate of 5% simple interest.

(4) Calculate the amount due after 9 years if Mary borrowed a sum of $5050 at a rate of 4% simple interest.

(5) Find the amount to be paid if William borrowed a sum of $5500 at 10% simple interest for 7 years.

(6) What amount does Christopher have to pay after 5 years if he takes a loan of $4000 at 10% simple interest?

(7) Susan took a loan of $5300 at the rate of 9% simple interest per annum. If he paid an amount of $9116 to clear the loan, then find the time period of the loan.

(8) Calculate the amount due after 10 years if Robert borrowed a sum of $5100 at a rate of 3% simple interest.

(9) What amount does Patricia have to pay after 5 years if he takes a loan of $3150 at 10% simple interest?

(10) Lisa took a loan of $6100 at the rate of 8% simple interest per annum. If he paid an amount of $10492 to clear the loan, then find the time period of the loan.