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) Michael took a loan of $4600 at the rate of 10% simple interest per annum. If he paid an amount of $7820 to clear the loan, then find the time period of the loan.

(2) What amount does Patricia have to pay after 6 years if he takes a loan of $3150 at 6% simple interest?

(3) What amount does Karen have to pay after 5 years if he takes a loan of $3950 at 6% simple interest?

(4) In how much time a principal of $3200 will amount to $3456 at a simple interest of 2% per annum?

(5) What amount will be due after 2 years if James borrowed a sum of $3000 at a 10% simple interest?

(6) Calculate the amount due if Joseph borrowed a sum of $3700 at 8% simple interest for 3 years.

(7) Find the amount to be paid if Richard borrowed a sum of $5600 at 5% simple interest for 8 years.

(8) Find the amount to be paid if Susan borrowed a sum of $5650 at 9% simple interest for 7 years.

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

(10) What amount does Sarah have to pay after 5 years if he takes a loan of $3850 at 4% simple interest?