Simple Interest
Math MCQs

Question :    Thomas took a loan of $5600 at the rate of 7% 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  8

Solution & Explanation

Solution

Given,

Principal (P) = $5600

Rate of Simple Interest (R) = 7% 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 × 7}

= ³¹³⁶⁰⁰/₃₉₂₀₀

= 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) = $5600

Rate of Simple Interest (R) = 7% 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 = 7% of Principal

= 7% of $5600

= ⁷/₁₀₀ × 5600

= ^{7 × 5600}/₁₀₀

= ³⁹²⁰⁰/₁₀₀ = 392

Thus, simple Interest for 1 year = $392

Now,

∵ If the simple Interest is $392, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₃₉₂ years

∴ If the simple Interest is $3136, then the time = ¹/₃₉₂ × 3136 years

= ^{1 × 3136}/₃₉₂ years

= ³¹³⁶/₃₉₂ = 8 years

Thus, time (T) = 8 years Answer

Similar Questions

(1) Calculate the amount due after 9 years if Robert borrowed a sum of $5100 at a rate of 9% simple interest.

(2) Daniel took a loan of $6200 at the rate of 7% simple interest per annum. If he paid an amount of $10540 to clear the loan, then find the time period of the loan.

(3) Jennifer took a loan of $4500 at the rate of 8% simple interest per annum. If he paid an amount of $7020 to clear the loan, then find the time period of the loan.

(4) Find the amount to be paid if Jessica borrowed a sum of $5750 at 2% simple interest for 8 years.

(5) What amount does Linda have to pay after 5 years if he takes a loan of $3350 at 9% simple interest?

(6) Sandra took a loan of $6900 at the rate of 7% simple interest per annum. If he paid an amount of $11247 to clear the loan, then find the time period of the loan.

(7) Robert took a loan of $4200 at the rate of 8% simple interest per annum. If he paid an amount of $7224 to clear the loan, then find the time period of the loan.

(8) If Richard borrowed $3600 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.

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

(10) What amount will be due after 2 years if Donald borrowed a sum of $3750 at a 10% simple interest?