Simple Interest
Math MCQs

Question :  ( 1 of 10 )  Anthony took a loan of $6600 at the rate of 8% simple interest per annum. If he paid an amount of $10296 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) = 8% per annum

Amount (A) = $10296

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 = $10296 – $6600 = $3696

Thus, Simple Interest = $3696

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 × 3696}/_{6600 × 8}

= ³⁶⁹⁶⁰⁰/₅₂₈₀₀

= 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) = 8% per annum

Simple Interest = $3696 (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 $6600

= ⁸/₁₀₀ × 6600

= ^{8 × 6600}/₁₀₀

= ⁵²⁸⁰⁰/₁₀₀ = 528

Thus, simple Interest for 1 year = $528

Now,

∵ If the simple Interest is $528, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₅₂₈ years

∴ If the simple Interest is $3696, then the time = ¹/₅₂₈ × 3696 years

= ^{1 × 3696}/₅₂₈ years

= ³⁶⁹⁶/₅₂₈ = 7 years

Thus, time (T) = 7 years Answer

Similar Questions

(1) Calculate the amount due after 10 years if Thomas borrowed a sum of $5800 at a rate of 3% simple interest.

(2) What amount will be due after 2 years if Kenneth borrowed a sum of $4000 at a 8% simple interest?

(3) If Linda paid $3752 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(4) Find the amount to be paid if David borrowed a sum of $5400 at 5% simple interest for 7 years.

(5) Calculate the amount due if Robert borrowed a sum of $3100 at 3% simple interest for 4 years.

(6) Calculate the amount due after 10 years if David borrowed a sum of $5400 at a rate of 9% simple interest.

(7) What amount does James have to pay after 6 years if he takes a loan of $3000 at 7% simple interest?

(8) What amount does Michael have to pay after 5 years if he takes a loan of $3300 at 8% simple interest?

(9) William took a loan of $5000 at the rate of 9% simple interest per annum. If he paid an amount of $8600 to clear the loan, then find the time period of the loan.

(10) James took a loan of $4000 at the rate of 6% simple interest per annum. If he paid an amount of $6400 to clear the loan, then find the time period of the loan.