Simple Interest
Math MCQs

Question :    Michael took a loan of $4600 at the rate of 6% simple interest per annum. If he paid an amount of $7360 to clear the loan, then find the time period of the loan.

Correct Answer  10

Solution & Explanation

Solution

Given,

Principal (P) = $4600

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

Amount (A) = $7360

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 = $7360 – $4600 = $2760

Thus, Simple Interest = $2760

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 × 2760}/_{4600 × 6}

= ²⁷⁶⁰⁰⁰/₂₇₆₀₀

= 10 years (using formula)

Thus, Time (T) = 10 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) = $4600

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

Simple Interest = $2760 (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 $4600

= ⁶/₁₀₀ × 4600

= ^{6 × 4600}/₁₀₀

= ²⁷⁶⁰⁰/₁₀₀ = 276

Thus, simple Interest for 1 year = $276

Now,

∵ If the simple Interest is $276, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₂₇₆ years

∴ If the simple Interest is $2760, then the time = ¹/₂₇₆ × 2760 years

= ^{1 × 2760}/₂₇₆ years

= ²⁷⁶⁰/₂₇₆ = 10 years

Thus, time (T) = 10 years Answer

Similar Questions

(1) What amount does Robert have to pay after 5 years if he takes a loan of $3100 at 4% simple interest?

(2) Calculate the amount due after 9 years if Elizabeth borrowed a sum of $5450 at a rate of 10% simple interest.

(3) If Robert paid $3472 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(4) How much loan did Joseph borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7125 to clear it?

(5) Calculate the amount due if William borrowed a sum of $3500 at 2% simple interest for 3 years.

(6) Find the amount to be paid if Sarah borrowed a sum of $5850 at 5% simple interest for 8 years.

(7) What amount does Michael have to pay after 6 years if he takes a loan of $3300 at 7% simple interest?

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

(9) Matthew took a loan of $6400 at the rate of 9% simple interest per annum. If he paid an amount of $9856 to clear the loan, then find the time period of the loan.

(10) Sandra took a loan of $6900 at the rate of 7% simple interest per annum. If he paid an amount of $11730 to clear the loan, then find the time period of the loan.