Simple Interest
Math MCQs

Question :    Richard took a loan of $5200 at the rate of 9% simple interest per annum. If he paid an amount of $9412 to clear the loan, then find the time period of the loan.

Correct Answer  9

Solution & Explanation

Solution

Given,

Principal (P) = $5200

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

Amount (A) = $9412

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 = $9412 – $5200 = $4212

Thus, Simple Interest = $4212

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 × 4212}/_{5200 × 9}

= ⁴²¹²⁰⁰/₄₆₈₀₀

= 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) = $5200

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

Simple Interest = $4212 (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 $5200

= ⁹/₁₀₀ × 5200

= ^{9 × 5200}/₁₀₀

= ⁴⁶⁸⁰⁰/₁₀₀ = 468

Thus, simple Interest for 1 year = $468

Now,

∵ If the simple Interest is $468, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₄₆₈ years

∴ If the simple Interest is $4212, then the time = ¹/₄₆₈ × 4212 years

= ^{1 × 4212}/₄₆₈ years

= ⁴²¹²/₄₆₈ = 9 years

Thus, time (T) = 9 years Answer

Similar Questions

(1) Robert took a loan of $4200 at the rate of 6% simple interest per annum. If he paid an amount of $6216 to clear the loan, then find the time period of the loan.

(2) Calculate the amount due after 9 years if Elizabeth borrowed a sum of $5450 at a rate of 10% simple interest.

(3) Donald took a loan of $7000 at the rate of 9% simple interest per annum. If he paid an amount of $11410 to clear the loan, then find the time period of the loan.

(4) Sandra took a loan of $6900 at the rate of 6% simple interest per annum. If he paid an amount of $10212 to clear the loan, then find the time period of the loan.

(5) Calculate the amount due after 9 years if Richard borrowed a sum of $5600 at a rate of 8% simple interest.

(6) Calculate the amount due if Robert borrowed a sum of $3100 at 7% simple interest for 4 years.

(7) What amount will be due after 2 years if Michael borrowed a sum of $3150 at a 10% simple interest?

(8) How much loan did Donald borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7800 to clear it?

(9) Robert took a loan of $4200 at the rate of 8% simple interest per annum. If he paid an amount of $6552 to clear the loan, then find the time period of the loan.

(10) Find the amount to be paid if Richard borrowed a sum of $5600 at 4% simple interest for 7 years.