Simple Interest
Math MCQs

Question :    Matthew took a loan of $6400 at the rate of 8% simple interest per annum. If he paid an amount of $10496 to clear the loan, then find the time period of the loan.

Correct Answer  8

Solution & Explanation

Solution

Given,

Principal (P) = $6400

Rate of Simple Interest (R) = 8% per annum

Amount (A) = $10496

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 = $10496 – $6400 = $4096

Thus, Simple Interest = $4096

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 × 4096}/_{6400 × 8}

= ⁴⁰⁹⁶⁰⁰/₅₁₂₀₀

= 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) = $6400

Rate of Simple Interest (R) = 8% per annum

Simple Interest = $4096 (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 = 8% of Principal

= 8% of $6400

= ⁸/₁₀₀ × 6400

= ^{8 × 6400}/₁₀₀

= ⁵¹²⁰⁰/₁₀₀ = 512

Thus, simple Interest for 1 year = $512

Now,

∵ If the simple Interest is $512, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₅₁₂ years

∴ If the simple Interest is $4096, then the time = ¹/₅₁₂ × 4096 years

= ^{1 × 4096}/₅₁₂ years

= ⁴⁰⁹⁶/₅₁₂ = 8 years

Thus, time (T) = 8 years Answer

Similar Questions

(1) James took a loan of $4000 at the rate of 7% simple interest per annum. If he paid an amount of $5960 to clear the loan, then find the time period of the loan.

(2) How much loan did Elizabeth borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6540 to clear it?

(3) Find the amount to be paid if Patricia borrowed a sum of $5150 at 6% simple interest for 7 years.

(4) Calculate the amount due after 10 years if Sarah borrowed a sum of $5850 at a rate of 9% simple interest.

(5) Calculate the amount due if Charles borrowed a sum of $3900 at 7% simple interest for 4 years.

(6) How much loan did Brian borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9000 to clear it?

(7) Find the amount to be paid if Christopher borrowed a sum of $6000 at 2% simple interest for 8 years.

(8) Find the amount to be paid if Mary borrowed a sum of $5050 at 3% simple interest for 7 years.

(9) Sarah had to pay $4312 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(10) Charles took a loan of $5800 at the rate of 10% simple interest per annum. If he paid an amount of $9860 to clear the loan, then find the time period of the loan.