Simple Interest
Math MCQs

Question :    Joseph took a loan of $5400 at the rate of 8% simple interest per annum. If he paid an amount of $9288 to clear the loan, then find the time period of the loan.

Correct Answer  9

Solution & Explanation

Solution

Given,

Principal (P) = $5400

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

Amount (A) = $9288

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 = $9288 – $5400 = $3888

Thus, Simple Interest = $3888

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 × 3888}/_{5400 × 8}

= ³⁸⁸⁸⁰⁰/₄₃₂₀₀

= 9 years (using formula)

Thus, Time (T) = 9 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) = $5400

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

Simple Interest = $3888 (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 $5400

= ⁸/₁₀₀ × 5400

= ^{8 × 5400}/₁₀₀

= ⁴³²⁰⁰/₁₀₀ = 432

Thus, simple Interest for 1 year = $432

Now,

∵ If the simple Interest is $432, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₄₃₂ years

∴ If the simple Interest is $3888, then the time = ¹/₄₃₂ × 3888 years

= ^{1 × 3888}/₄₃₂ years

= ³⁸⁸⁸/₄₃₂ = 9 years

Thus, time (T) = 9 years Answer

Similar Questions

(1) Calculate the amount due after 9 years if Patricia borrowed a sum of $5150 at a rate of 2% simple interest.

(2) What amount does Michael have to pay after 6 years if he takes a loan of $3300 at 2% simple interest?

(3) How much loan did Michelle borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8687.5 to clear it?

(4) What amount does Karen have to pay after 6 years if he takes a loan of $3950 at 3% simple interest?

(5) Find the amount to be paid if John borrowed a sum of $5200 at 6% simple interest for 7 years.

(6) Calculate the amount due if William borrowed a sum of $3500 at 6% simple interest for 4 years.

(7) If Mary borrowed $3050 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.

(8) Calculate the amount due after 9 years if David borrowed a sum of $5400 at a rate of 2% simple interest.

(9) Lisa took a loan of $6100 at the rate of 9% simple interest per annum. If he paid an amount of $11041 to clear the loan, then find the time period of the loan.

(10) What amount does Joseph have to pay after 6 years if he takes a loan of $3700 at 7% simple interest?