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 $10880 to clear the loan, then find the time period of the loan.

Correct Answer  7

Solution & Explanation

Solution

Given,

Principal (P) = $6400

Rate of Simple Interest (R) = 10% per annum

Amount (A) = $10880

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 = $10880 – $6400 = $4480

Thus, Simple Interest = $4480

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 × 4480}/_{6400 × 10}

= ⁴⁴⁸⁰⁰⁰/₆₄₀₀₀

= 7 years (using formula)

Thus, Time (T) = 7 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 = $4480 (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 $4480, then the time = ¹/₆₄₀ × 4480 years

= ^{1 × 4480}/₆₄₀ years

= ⁴⁴⁸⁰/₆₄₀ = 7 years

Thus, time (T) = 7 years Answer

Similar Questions

(1) Linda took a loan of $4700 at the rate of 6% simple interest per annum. If he paid an amount of $6674 to clear the loan, then find the time period of the loan.

(2) Thomas took a loan of $5600 at the rate of 10% simple interest per annum. If he paid an amount of $10080 to clear the loan, then find the time period of the loan.

(3) Kimberly had to pay $5068.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(4) If Michael paid $3696 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(5) Christopher took a loan of $6000 at the rate of 10% simple interest per annum. If he paid an amount of $11400 to clear the loan, then find the time period of the loan.

(6) Donald had to pay $4770 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(7) Calculate the amount due after 10 years if Sarah borrowed a sum of $5850 at a rate of 7% simple interest.

(8) Calculate the amount due after 10 years if David borrowed a sum of $5400 at a rate of 8% simple interest.

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

(10) Paul had to pay $5264 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.