Simple Interest
Math MCQs

Question :    Barbara took a loan of $5100 at the rate of 9% simple interest per annum. If he paid an amount of $9231 to clear the loan, then find the time period of the loan.

Correct Answer  9

Solution & Explanation

Solution

Given,

Principal (P) = $5100

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

Amount (A) = $9231

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 = $9231 – $5100 = $4131

Thus, Simple Interest = $4131

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 × 4131}/_{5100 × 9}

= ⁴¹³¹⁰⁰/₄₅₉₀₀

= 9 years (using formula)

Thus, Time (T) = 9 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) = $5100

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

Simple Interest = $4131 (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 $5100

= ⁹/₁₀₀ × 5100

= ^{9 × 5100}/₁₀₀

= ⁴⁵⁹⁰⁰/₁₀₀ = 459

Thus, simple Interest for 1 year = $459

Now,

∵ If the simple Interest is $459, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₄₅₉ years

∴ If the simple Interest is $4131, then the time = ¹/₄₅₉ × 4131 years

= ^{1 × 4131}/₄₅₉ years

= ⁴¹³¹/₄₅₉ = 9 years

Thus, time (T) = 9 years Answer

Similar Questions

(1) Anthony took a loan of $6600 at the rate of 10% simple interest per annum. If he paid an amount of $12540 to clear the loan, then find the time period of the loan.

(2) Calculate the amount due if Charles borrowed a sum of $3900 at 8% simple interest for 3 years.

(3) How much loan did Susan borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6215 to clear it?

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

(5) Find the amount to be paid if William borrowed a sum of $5500 at 10% simple interest for 8 years.

(6) Find the amount to be paid if Thomas borrowed a sum of $5800 at 5% simple interest for 7 years.

(7) Calculate the amount due after 9 years if Michael borrowed a sum of $5300 at a rate of 5% simple interest.

(8) If Lisa paid $4860 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

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

(10) Matthew took a loan of $6400 at the rate of 7% simple interest per annum. If he paid an amount of $9984 to clear the loan, then find the time period of the loan.