Simple Interest
Math MCQs

Question :    Mark took a loan of $6800 at the rate of 9% simple interest per annum. If he paid an amount of $12920 to clear the loan, then find the time period of the loan.

Correct Answer  10

Solution & Explanation

Solution

Given,

Principal (P) = $6800

Rate of Simple Interest (R) = 9% per annum

Amount (A) = $12920

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 = $12920 – $6800 = $6120

Thus, Simple Interest = $6120

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 × 6120}/_{6800 × 9}

= ⁶¹²⁰⁰⁰/₆₁₂₀₀

= 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) = $6800

Rate of Simple Interest (R) = 9% per annum

Simple Interest = $6120 (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 = 9% of Principal

= 9% of $6800

= ⁹/₁₀₀ × 6800

= ^{9 × 6800}/₁₀₀

= ⁶¹²⁰⁰/₁₀₀ = 612

Thus, simple Interest for 1 year = $612

Now,

∵ If the simple Interest is $612, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₆₁₂ years

∴ If the simple Interest is $6120, then the time = ¹/₆₁₂ × 6120 years

= ^{1 × 6120}/₆₁₂ years

= ⁶¹²⁰/₆₁₂ = 10 years

Thus, time (T) = 10 years Answer

Similar Questions

(1) Susan took a loan of $5300 at the rate of 6% simple interest per annum. If he paid an amount of $7208 to clear the loan, then find the time period of the loan.

(2) If Andrew paid $5184 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(3) Joshua had to pay $5488 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(4) Calculate the amount due if Richard borrowed a sum of $3600 at 9% simple interest for 3 years.

(5) How much loan did Daniel borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7625 to clear it?

(6) If Patricia paid $3780 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(7) What amount will be due after 2 years if Anthony borrowed a sum of $3650 at a 5% simple interest?

(8) Find the amount to be paid if Joseph borrowed a sum of $5700 at 4% simple interest for 7 years.

(9) How much loan did Jennifer borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5775 to clear it?

(10) Find the amount to be paid if David borrowed a sum of $5400 at 8% simple interest for 7 years.