Simple Interest
Math MCQs

Question :    Elizabeth took a loan of $4900 at the rate of 10% simple interest per annum. If he paid an amount of $8330 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) = 10% per annum

Amount (A) = $8330

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 = $8330 – $4900 = $3430

Thus, Simple Interest = $3430

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 × 3430}/_{4900 × 10}

= ³⁴³⁰⁰⁰/₄₉₀₀₀

= 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) = 10% per annum

Simple Interest = $3430 (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 = 10% of Principal

= 10% of $4900

= ¹⁰/₁₀₀ × 4900

= ^{10 × 4900}/₁₀₀

= ⁴⁹⁰⁰⁰/₁₀₀ = 490

Thus, simple Interest for 1 year = $490

Now,

∵ If the simple Interest is $490, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₄₉₀ years

∴ If the simple Interest is $3430, then the time = ¹/₄₉₀ × 3430 years

= ^{1 × 3430}/₄₉₀ years

= ³⁴³⁰/₄₉₀ = 7 years

Thus, time (T) = 7 years Answer

Similar Questions

(1) Calculate the amount due after 9 years if Richard borrowed a sum of $5600 at a rate of 10% simple interest.

(2) Find the amount to be paid if Thomas borrowed a sum of $5800 at 8% simple interest for 8 years.

(3) Sandra took a loan of $6900 at the rate of 10% simple interest per annum. If he paid an amount of $13800 to clear the loan, then find the time period of the loan.

(4) Calculate the amount due if William borrowed a sum of $3500 at 4% simple interest for 4 years.

(5) Karen took a loan of $5900 at the rate of 10% simple interest per annum. If he paid an amount of $10030 to clear the loan, then find the time period of the loan.

(6) Calculate the amount due if Joseph borrowed a sum of $3700 at 8% simple interest for 3 years.

(7) What amount does Michael have to pay after 6 years if he takes a loan of $3300 at 8% simple interest?

(8) Calculate the amount due after 10 years if Thomas borrowed a sum of $5800 at a rate of 5% simple interest.

(9) Calculate the amount due if Sarah borrowed a sum of $3850 at 2% simple interest for 3 years.

(10) How much loan did Kimberly borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8312.5 to clear it?