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 does Susan have to pay after 6 years if he takes a loan of $3650 at 8% simple interest?

(2) John took a loan of $4400 at the rate of 9% simple interest per annum. If he paid an amount of $7964 to clear the loan, then find the time period of the loan.

(3) Calculate the amount due after 10 years if Charles borrowed a sum of $5900 at a rate of 2% simple interest.

(4) What amount does Robert have to pay after 6 years if he takes a loan of $3100 at 5% simple interest?

(5) Robert took a loan of $4200 at the rate of 10% simple interest per annum. If he paid an amount of $7140 to clear the loan, then find the time period of the loan.

(6) Find the amount to be paid if Joseph borrowed a sum of $5700 at 6% simple interest for 7 years.

(7) Calculate the amount due if Michael borrowed a sum of $3300 at 5% simple interest for 4 years.

(8) How much loan did John borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6500 to clear it?

(9) Find the amount to be paid if Michael borrowed a sum of $5300 at 2% simple interest for 7 years.

(10) Calculate the amount due after 9 years if Jessica borrowed a sum of $5750 at a rate of 9% simple interest.