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 $10240 to clear the loan, then find the time period of the loan.

Correct Answer  10

Solution & Explanation

Solution

Given,

Principal (P) = $6400

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

Amount (A) = $10240

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 = $10240 – $6400 = $3840

Thus, Simple Interest = $3840

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 × 3840}/_{6400 × 6}

= ³⁸⁴⁰⁰⁰/₃₈₄₀₀

= 10 years (using formula)

Thus, Time (T) = 10 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 = $3840 (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 $3840, then the time = ¹/₃₈₄ × 3840 years

= ^{1 × 3840}/₃₈₄ years

= ³⁸⁴⁰/₃₈₄ = 10 years

Thus, time (T) = 10 years Answer

Similar Questions

(1) Calculate the amount due after 9 years if James borrowed a sum of $5000 at a rate of 4% simple interest.

(2) How much loan did Timothy borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9250 to clear it?

(3) What amount does James have to pay after 5 years if he takes a loan of $3000 at 9% simple interest?

(4) Joseph took a loan of $5400 at the rate of 6% simple interest per annum. If he paid an amount of $7992 to clear the loan, then find the time period of the loan.

(5) What amount will be due after 2 years if David borrowed a sum of $3200 at a 5% simple interest?

(6) Richard had to pay $4032 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(7) What amount will be due after 2 years if Mark borrowed a sum of $3700 at a 9% simple interest?

(8) Jennifer took a loan of $4500 at the rate of 10% simple interest per annum. If he paid an amount of $8550 to clear the loan, then find the time period of the loan.

(9) Calculate the amount due if Karen borrowed a sum of $3950 at 5% simple interest for 3 years.

(10) Find the amount to be paid if Patricia borrowed a sum of $5150 at 6% simple interest for 8 years.