Simple Interest
Math MCQs

Question :    Matthew took a loan of $6400 at the rate of 6% simple interest per annum. If he paid an amount of $8704 to clear the loan, then find the time period of the loan.

Correct Answer  6

Solution & Explanation

Solution

Given,

Principal (P) = $6400

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

Amount (A) = $8704

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 = $8704 – $6400 = $2304

Thus, Simple Interest = $2304

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 × 2304}/_{6400 × 6}

= ²³⁰⁴⁰⁰/₃₈₄₀₀

= 6 years (using formula)

Thus, Time (T) = 6 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) = $6400

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

Simple Interest = $2304 (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 $6400

= ⁶/₁₀₀ × 6400

= ^{6 × 6400}/₁₀₀

= ³⁸⁴⁰⁰/₁₀₀ = 384

Thus, simple Interest for 1 year = $384

Now,

∵ If the simple Interest is $384, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₃₈₄ years

∴ If the simple Interest is $2304, then the time = ¹/₃₈₄ × 2304 years

= ^{1 × 2304}/₃₈₄ years

= ²³⁰⁴/₃₈₄ = 6 years

Thus, time (T) = 6 years Answer

Similar Questions

(1) Calculate the amount due after 10 years if John borrowed a sum of $5200 at a rate of 7% simple interest.

(2) Find the amount to be paid if Richard borrowed a sum of $5600 at 3% simple interest for 7 years.

(3) How much loan did Kevin borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8875 to clear it?

(4) Find the amount to be paid if Charles borrowed a sum of $5900 at 5% simple interest for 7 years.

(5) In how much time a principal of $3200 will amount to $3680 at a simple interest of 5% per annum?

(6) Anthony took a loan of $6600 at the rate of 7% simple interest per annum. If he paid an amount of $11220 to clear the loan, then find the time period of the loan.

(7) What amount will be due after 2 years if Joseph borrowed a sum of $3350 at a 6% simple interest?

(8) Barbara took a loan of $5100 at the rate of 10% simple interest per annum. If he paid an amount of $9690 to clear the loan, then find the time period of the loan.

(9) How much loan did Deborah borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9312.5 to clear it?

(10) Find the amount to be paid if Patricia borrowed a sum of $5150 at 8% simple interest for 7 years.