Simple Interest
Math MCQs

Question :    Betty took a loan of $6500 at the rate of 10% simple interest per annum. If he paid an amount of $10400 to clear the loan, then find the time period of the loan.

Correct Answer  6

Solution & Explanation

Solution

Given,

Principal (P) = $6500

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

Amount (A) = $10400

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 = $10400 – $6500 = $3900

Thus, Simple Interest = $3900

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 × 3900}/_{6500 × 10}

= ³⁹⁰⁰⁰⁰/₆₅₀₀₀

= 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) = $6500

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

Simple Interest = $3900 (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 $6500

= ¹⁰/₁₀₀ × 6500

= ^{10 × 6500}/₁₀₀

= ⁶⁵⁰⁰⁰/₁₀₀ = 650

Thus, simple Interest for 1 year = $650

Now,

∵ If the simple Interest is $650, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₆₅₀ years

∴ If the simple Interest is $3900, then the time = ¹/₆₅₀ × 3900 years

= ^{1 × 3900}/₆₅₀ years

= ³⁹⁰⁰/₆₅₀ = 6 years

Thus, time (T) = 6 years Answer

Similar Questions

(1) Calculate the amount due after 10 years if Susan borrowed a sum of $5650 at a rate of 9% simple interest.

(2) Sandra took a loan of $6900 at the rate of 10% simple interest per annum. If he paid an amount of $11730 to clear the loan, then find the time period of the loan.

(3) Find the amount to be paid if Jessica borrowed a sum of $5750 at 8% simple interest for 7 years.

(4) Karen took a loan of $5900 at the rate of 8% simple interest per annum. If he paid an amount of $8732 to clear the loan, then find the time period of the loan.

(5) Calculate the amount due if Jessica borrowed a sum of $3750 at 6% simple interest for 4 years.

(6) Calculate the amount due if Joseph borrowed a sum of $3700 at 2% simple interest for 4 years.

(7) Calculate the amount due if Karen borrowed a sum of $3950 at 6% simple interest for 4 years.

(8) Find the amount to be paid if Richard borrowed a sum of $5600 at 5% simple interest for 7 years.

(9) Calculate the amount due if Mary borrowed a sum of $3050 at 6% simple interest for 3 years.

(10) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 10% simple interest for 4 years.