Simple Interest
Math MCQs

Question :    John took a loan of $4400 at the rate of 6% simple interest per annum. If he paid an amount of $6248 to clear the loan, then find the time period of the loan.

Correct Answer  7

Solution & Explanation

Solution

Given,

Principal (P) = $4400

Rate of Simple Interest (R) = 6% per annum

Amount (A) = $6248

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 = $6248 – $4400 = $1848

Thus, Simple Interest = $1848

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 × 1848}/_{4400 × 6}

= ¹⁸⁴⁸⁰⁰/₂₆₄₀₀

= 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) = $4400

Rate of Simple Interest (R) = 6% per annum

Simple Interest = $1848 (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 = 6% of Principal

= 6% of $4400

= ⁶/₁₀₀ × 4400

= ^{6 × 4400}/₁₀₀

= ²⁶⁴⁰⁰/₁₀₀ = 264

Thus, simple Interest for 1 year = $264

Now,

∵ If the simple Interest is $264, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₂₆₄ years

∴ If the simple Interest is $1848, then the time = ¹/₂₆₄ × 1848 years

= ^{1 × 1848}/₂₆₄ years

= ¹⁸⁴⁸/₂₆₄ = 7 years

Thus, time (T) = 7 years Answer

Similar Questions

(1) What amount will be due after 2 years if William borrowed a sum of $3250 at a 5% simple interest?

(2) Calculate the amount due after 9 years if Susan borrowed a sum of $5650 at a rate of 5% simple interest.

(3) Calculate the amount due if David borrowed a sum of $3400 at 8% simple interest for 3 years.

(4) How much loan did Jennifer borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6037.5 to clear it?

(5) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 7% simple interest?

(6) If Betty paid $4760 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(7) Find the amount to be paid if Barbara borrowed a sum of $5550 at 6% simple interest for 7 years.

(8) Calculate the amount due after 9 years if Robert borrowed a sum of $5100 at a rate of 4% simple interest.

(9) Charles took a loan of $5800 at the rate of 7% simple interest per annum. If he paid an amount of $9048 to clear the loan, then find the time period of the loan.

(10) Betty took a loan of $6500 at the rate of 7% simple interest per annum. If he paid an amount of $10595 to clear the loan, then find the time period of the loan.