Simple Interest
Math MCQs

Question :    Thomas took a loan of $5600 at the rate of 8% simple interest per annum. If he paid an amount of $8736 to clear the loan, then find the time period of the loan.

Correct Answer  7

Solution & Explanation

Solution

Given,

Principal (P) = $5600

Rate of Simple Interest (R) = 8% per annum

Amount (A) = $8736

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 = $8736 – $5600 = $3136

Thus, Simple Interest = $3136

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 × 3136}/_{5600 × 8}

= ³¹³⁶⁰⁰/₄₄₈₀₀

= 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) = $5600

Rate of Simple Interest (R) = 8% per annum

Simple Interest = $3136 (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 = 8% of Principal

= 8% of $5600

= ⁸/₁₀₀ × 5600

= ^{8 × 5600}/₁₀₀

= ⁴⁴⁸⁰⁰/₁₀₀ = 448

Thus, simple Interest for 1 year = $448

Now,

∵ If the simple Interest is $448, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₄₄₈ years

∴ If the simple Interest is $3136, then the time = ¹/₄₄₈ × 3136 years

= ^{1 × 3136}/₄₄₈ years

= ³¹³⁶/₄₄₈ = 7 years

Thus, time (T) = 7 years Answer

Similar Questions

(1) Calculate the amount due if Richard borrowed a sum of $3600 at 7% simple interest for 4 years.

(2) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 5% simple interest for 8 years.

(3) Donald took a loan of $7000 at the rate of 9% simple interest per annum. If he paid an amount of $11410 to clear the loan, then find the time period of the loan.

(4) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 10% simple interest for 3 years.

(5) Calculate the amount due after 9 years if John borrowed a sum of $5200 at a rate of 9% simple interest.

(6) William took a loan of $5000 at the rate of 6% simple interest per annum. If he paid an amount of $8000 to clear the loan, then find the time period of the loan.

(7) In how much time a principal of $3000 will amount to $3180 at a simple interest of 2% per annum?

(8) Jessica took a loan of $5500 at the rate of 9% simple interest per annum. If he paid an amount of $9955 to clear the loan, then find the time period of the loan.

(9) Calculate the amount due if Patricia borrowed a sum of $3150 at 3% simple interest for 3 years.

(10) What amount will be due after 2 years if James borrowed a sum of $3000 at a 4% simple interest?