Simple Interest
Math MCQs

Question :    Matthew took a loan of $6400 at the rate of 10% 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  6

Solution & Explanation

Solution

Given,

Principal (P) = $6400

Rate of Simple Interest (R) = 10% 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 × 10}

= ³⁸⁴⁰⁰⁰/₆₄₀₀₀

= 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) = 10% 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 = 10% of Principal

= 10% of $6400

= ¹⁰/₁₀₀ × 6400

= ^{10 × 6400}/₁₀₀

= ⁶⁴⁰⁰⁰/₁₀₀ = 640

Thus, simple Interest for 1 year = $640

Now,

∵ If the simple Interest is $640, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₆₄₀ years

∴ If the simple Interest is $3840, then the time = ¹/₆₄₀ × 3840 years

= ^{1 × 3840}/₆₄₀ years

= ³⁸⁴⁰/₆₄₀ = 6 years

Thus, time (T) = 6 years Answer

Similar Questions

(1) What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 8% simple interest?

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

(3) How much loan did Emily borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8100 to clear it?

(4) If Mary paid $3416 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(5) Anthony took a loan of $6600 at the rate of 9% simple interest per annum. If he paid an amount of $10758 to clear the loan, then find the time period of the loan.

(6) What amount will be due after 2 years if William borrowed a sum of $3250 at a 9% simple interest?

(7) Linda took a loan of $4700 at the rate of 6% simple interest per annum. If he paid an amount of $7520 to clear the loan, then find the time period of the loan.

(8) Calculate the amount due after 10 years if Mary borrowed a sum of $5050 at a rate of 8% simple interest.

(9) Find the amount to be paid if Karen borrowed a sum of $5950 at 7% simple interest for 7 years.

(10) Richard took a loan of $5200 at the rate of 8% simple interest per annum. If he paid an amount of $9360 to clear the loan, then find the time period of the loan.