Simple Interest
Math MCQs

Question :    Anthony took a loan of $6600 at the rate of 6% simple interest per annum. If he paid an amount of $9372 to clear the loan, then find the time period of the loan.

Correct Answer  7

Solution & Explanation

Solution

Given,

Principal (P) = $6600

Rate of Simple Interest (R) = 6% per annum

Amount (A) = $9372

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 = $9372 – $6600 = $2772

Thus, Simple Interest = $2772

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 × 2772}/_{6600 × 6}

= ²⁷⁷²⁰⁰/₃₉₆₀₀

= 7 years (using formula)

Thus, Time (T) = 7 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) = $6600

Rate of Simple Interest (R) = 6% per annum

Simple Interest = $2772 (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 = 6% of Principal

= 6% of $6600

= ⁶/₁₀₀ × 6600

= ^{6 × 6600}/₁₀₀

= ³⁹⁶⁰⁰/₁₀₀ = 396

Thus, simple Interest for 1 year = $396

Now,

∵ If the simple Interest is $396, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₃₉₆ years

∴ If the simple Interest is $2772, then the time = ¹/₃₉₆ × 2772 years

= ^{1 × 2772}/₃₉₆ years

= ²⁷⁷²/₃₉₆ = 7 years

Thus, time (T) = 7 years Answer

Similar Questions

(1) John took a loan of $4400 at the rate of 8% simple interest per annum. If he paid an amount of $7568 to clear the loan, then find the time period of the loan.

(2) What amount does Christopher have to pay after 5 years if he takes a loan of $4000 at 7% simple interest?

(3) Calculate the amount due if Sarah borrowed a sum of $3850 at 3% simple interest for 4 years.

(4) Calculate the amount due if Robert borrowed a sum of $3100 at 8% simple interest for 4 years.

(5) Karen took a loan of $5900 at the rate of 6% simple interest per annum. If he paid an amount of $8732 to clear the loan, then find the time period of the loan.

(6) Richard took a loan of $5200 at the rate of 6% simple interest per annum. If he paid an amount of $7696 to clear the loan, then find the time period of the loan.

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

(8) Calculate the amount due if James borrowed a sum of $3000 at 8% simple interest for 3 years.

(9) Sandra took a loan of $6900 at the rate of 10% simple interest per annum. If he paid an amount of $13110 to clear the loan, then find the time period of the loan.

(10) Betty took a loan of $6500 at the rate of 8% simple interest per annum. If he paid an amount of $11700 to clear the loan, then find the time period of the loan.