Simple Interest
Math MCQs

Question :    John took a loan of $4400 at the rate of 7% simple interest per annum. If he paid an amount of $6864 to clear the loan, then find the time period of the loan.

Correct Answer  8

Solution & Explanation

Solution

Given,

Principal (P) = $4400

Rate of Simple Interest (R) = 7% per annum

Amount (A) = $6864

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 = $6864 – $4400 = $2464

Thus, Simple Interest = $2464

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 × 2464}/_{4400 × 7}

= ²⁴⁶⁴⁰⁰/₃₀₈₀₀

= 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) = $4400

Rate of Simple Interest (R) = 7% per annum

Simple Interest = $2464 (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 = 7% of Principal

= 7% of $4400

= ⁷/₁₀₀ × 4400

= ^{7 × 4400}/₁₀₀

= ³⁰⁸⁰⁰/₁₀₀ = 308

Thus, simple Interest for 1 year = $308

Now,

∵ If the simple Interest is $308, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₃₀₈ years

∴ If the simple Interest is $2464, then the time = ¹/₃₀₈ × 2464 years

= ^{1 × 2464}/₃₀₈ years

= ²⁴⁶⁴/₃₀₈ = 8 years

Thus, time (T) = 8 years Answer

Similar Questions

(1) What amount will be due after 2 years if Michael borrowed a sum of $3150 at a 7% simple interest?

(2) Calculate the amount due after 10 years if Christopher borrowed a sum of $6000 at a rate of 4% simple interest.

(3) What amount will be due after 2 years if Mark borrowed a sum of $3700 at a 6% simple interest?

(4) Calculate the amount due if Karen borrowed a sum of $3950 at 7% simple interest for 3 years.

(5) How much loan did Christopher borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6600 to clear it?

(6) Calculate the amount due after 10 years if Richard borrowed a sum of $5600 at a rate of 4% simple interest.

(7) Calculate the amount due if Michael borrowed a sum of $3300 at 5% simple interest for 3 years.

(8) What amount will be due after 2 years if Paul borrowed a sum of $3850 at a 9% simple interest?

(9) What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 3% simple interest?

(10) Matthew took a loan of $6400 at the rate of 7% simple interest per annum. If he paid an amount of $10432 to clear the loan, then find the time period of the loan.