Simple Interest
Math MCQs

Question :    Sandra took a loan of $6900 at the rate of 9% simple interest per annum. If he paid an amount of $11868 to clear the loan, then find the time period of the loan.

Correct Answer  8

Solution & Explanation

Solution

Given,

Principal (P) = $6900

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

Amount (A) = $11868

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 = $11868 – $6900 = $4968

Thus, Simple Interest = $4968

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 × 4968}/_{6900 × 9}

= ⁴⁹⁶⁸⁰⁰/₆₂₁₀₀

= 8 years (using formula)

Thus, Time (T) = 8 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) = 9% per annum

Simple Interest = $4968 (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 $6900

= ⁹/₁₀₀ × 6900

= ^{9 × 6900}/₁₀₀

= ⁶²¹⁰⁰/₁₀₀ = 621

Thus, simple Interest for 1 year = $621

Now,

∵ If the simple Interest is $621, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₆₂₁ years

∴ If the simple Interest is $4968, then the time = ¹/₆₂₁ × 4968 years

= ^{1 × 4968}/₆₂₁ years

= ⁴⁹⁶⁸/₆₂₁ = 8 years

Thus, time (T) = 8 years Answer

Similar Questions

(1) William took a loan of $5000 at the rate of 10% simple interest per annum. If he paid an amount of $8000 to clear the loan, then find the time period of the loan.

(2) Calculate the amount due after 10 years if Michael borrowed a sum of $5300 at a rate of 2% simple interest.

(3) Calculate the amount due after 9 years if James borrowed a sum of $5000 at a rate of 3% simple interest.

(4) Mark took a loan of $6800 at the rate of 8% simple interest per annum. If he paid an amount of $10608 to clear the loan, then find the time period of the loan.

(5) Find the amount to be paid if Susan borrowed a sum of $5650 at 3% simple interest for 7 years.

(6) Calculate the amount due if William borrowed a sum of $3500 at 10% simple interest for 3 years.

(7) Barbara took a loan of $5100 at the rate of 7% simple interest per annum. If he paid an amount of $8313 to clear the loan, then find the time period of the loan.

(8) Elizabeth took a loan of $4900 at the rate of 10% simple interest per annum. If he paid an amount of $7840 to clear the loan, then find the time period of the loan.

(9) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 4% simple interest for 8 years.

(10) Calculate the amount due if Linda borrowed a sum of $3350 at 4% simple interest for 4 years.