Simple Interest
Math MCQs

Question :    Sandra took a loan of $6900 at the rate of 10% simple interest per annum. If he paid an amount of $11040 to clear the loan, then find the time period of the loan.

Correct Answer  6

Solution & Explanation

Solution

Given,

Principal (P) = $6900

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

Amount (A) = $11040

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 = $11040 – $6900 = $4140

Thus, Simple Interest = $4140

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 × 4140}/_{6900 × 10}

= ⁴¹⁴⁰⁰⁰/₆₉₀₀₀

= 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) = $6900

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

Simple Interest = $4140 (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 $6900

= ¹⁰/₁₀₀ × 6900

= ^{10 × 6900}/₁₀₀

= ⁶⁹⁰⁰⁰/₁₀₀ = 690

Thus, simple Interest for 1 year = $690

Now,

∵ If the simple Interest is $690, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₆₉₀ years

∴ If the simple Interest is $4140, then the time = ¹/₆₉₀ × 4140 years

= ^{1 × 4140}/₆₉₀ years

= ⁴¹⁴⁰/₆₉₀ = 6 years

Thus, time (T) = 6 years Answer

Similar Questions

(1) Calculate the amount due if William borrowed a sum of $3500 at 3% simple interest for 4 years.

(2) Find the amount to be paid if Thomas borrowed a sum of $5800 at 8% simple interest for 8 years.

(3) What amount does William have to pay after 6 years if he takes a loan of $3500 at 6% simple interest?

(4) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 8% simple interest?

(5) Thomas took a loan of $5600 at the rate of 10% simple interest per annum. If he paid an amount of $11200 to clear the loan, then find the time period of the loan.

(6) Calculate the amount due if Christopher borrowed a sum of $4000 at 4% simple interest for 4 years.

(7) Find the amount to be paid if Patricia borrowed a sum of $5150 at 4% simple interest for 7 years.

(8) Calculate the amount due after 9 years if Elizabeth borrowed a sum of $5450 at a rate of 6% simple interest.

(9) What amount does Christopher have to pay after 6 years if he takes a loan of $4000 at 6% simple interest?

(10) Sarah took a loan of $5700 at the rate of 9% simple interest per annum. If he paid an amount of $9291 to clear the loan, then find the time period of the loan.