Simple Interest
Math MCQs

Question :    Lisa took a loan of $6100 at the rate of 8% simple interest per annum. If he paid an amount of $10004 to clear the loan, then find the time period of the loan.

Correct Answer  8

Solution & Explanation

Solution

Given,

Principal (P) = $6100

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

Amount (A) = $10004

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 = $10004 – $6100 = $3904

Thus, Simple Interest = $3904

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 × 3904}/_{6100 × 8}

= ³⁹⁰⁴⁰⁰/₄₈₈₀₀

= 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) = $6100

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

Simple Interest = $3904 (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 $6100

= ⁸/₁₀₀ × 6100

= ^{8 × 6100}/₁₀₀

= ⁴⁸⁸⁰⁰/₁₀₀ = 488

Thus, simple Interest for 1 year = $488

Now,

∵ If the simple Interest is $488, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₄₈₈ years

∴ If the simple Interest is $3904, then the time = ¹/₄₈₈ × 3904 years

= ^{1 × 3904}/₄₈₈ years

= ³⁹⁰⁴/₄₈₈ = 8 years

Thus, time (T) = 8 years Answer

Similar Questions

(1) What amount will be due after 2 years if Michael borrowed a sum of $3150 at a 4% simple interest?

(2) Calculate the amount due after 9 years if Sarah borrowed a sum of $5850 at a rate of 5% simple interest.

(3) Matthew took a loan of $6400 at the rate of 6% simple interest per annum. If he paid an amount of $8704 to clear the loan, then find the time period of the loan.

(4) Margaret took a loan of $6700 at the rate of 9% simple interest per annum. If he paid an amount of $12730 to clear the loan, then find the time period of the loan.

(5) Mark took a loan of $6800 at the rate of 9% simple interest per annum. If he paid an amount of $11696 to clear the loan, then find the time period of the loan.

(6) Find the amount to be paid if Michael borrowed a sum of $5300 at 8% simple interest for 8 years.

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

(8) Linda took a loan of $4700 at the rate of 6% simple interest per annum. If he paid an amount of $7238 to clear the loan, then find the time period of the loan.

(9) Calculate the amount due after 9 years if Richard borrowed a sum of $5600 at a rate of 8% simple interest.

(10) How much loan did Margaret borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7620 to clear it?