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) Find the amount to be paid if Charles borrowed a sum of $5900 at 6% simple interest for 8 years.

(2) What amount does Robert have to pay after 6 years if he takes a loan of $3100 at 2% simple interest?

(3) Robert took a loan of $4200 at the rate of 10% simple interest per annum. If he paid an amount of $7980 to clear the loan, then find the time period of the loan.

(4) What amount will be due after 2 years if Donald borrowed a sum of $3750 at a 8% simple interest?

(5) Find the amount to be paid if Sarah borrowed a sum of $5850 at 5% simple interest for 7 years.

(6) Calculate the amount due after 9 years if Karen borrowed a sum of $5950 at a rate of 4% simple interest.

(7) Michael took a loan of $4600 at the rate of 7% simple interest per annum. If he paid an amount of $6854 to clear the loan, then find the time period of the loan.

(8) Margaret took a loan of $6700 at the rate of 7% simple interest per annum. If he paid an amount of $9983 to clear the loan, then find the time period of the loan.

(9) What amount will be due after 2 years if Joseph borrowed a sum of $3350 at a 6% simple interest?

(10) What amount will be due after 2 years if Michael borrowed a sum of $3150 at a 6% simple interest?