Simple Interest
Math MCQs

Question :    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.

Correct Answer  10

Solution & Explanation

Solution

Given,

Principal (P) = $6700

Rate of Simple Interest (R) = 9% per annum

Amount (A) = $12730

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 = $12730 – $6700 = $6030

Thus, Simple Interest = $6030

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 × 6030}/_{6700 × 9}

= ⁶⁰³⁰⁰⁰/₆₀₃₀₀

= 10 years (using formula)

Thus, Time (T) = 10 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) = $6700

Rate of Simple Interest (R) = 9% per annum

Simple Interest = $6030 (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 = 9% of Principal

= 9% of $6700

= ⁹/₁₀₀ × 6700

= ^{9 × 6700}/₁₀₀

= ⁶⁰³⁰⁰/₁₀₀ = 603

Thus, simple Interest for 1 year = $603

Now,

∵ If the simple Interest is $603, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₆₀₃ years

∴ If the simple Interest is $6030, then the time = ¹/₆₀₃ × 6030 years

= ^{1 × 6030}/₆₀₃ years

= ⁶⁰³⁰/₆₀₃ = 10 years

Thus, time (T) = 10 years Answer

Similar Questions

(1) What amount will be due after 2 years if Joshua borrowed a sum of $3950 at a 10% simple interest?

(2) Barbara took a loan of $5100 at the rate of 7% simple interest per annum. If he paid an amount of $8670 to clear the loan, then find the time period of the loan.

(3) Calculate the amount due if Christopher borrowed a sum of $4000 at 6% simple interest for 4 years.

(4) Find the amount to be paid if James borrowed a sum of $5000 at 5% simple interest for 8 years.

(5) What amount does Mary have to pay after 5 years if he takes a loan of $3050 at 10% simple interest?

(6) Find the amount to be paid if Joseph borrowed a sum of $5700 at 8% simple interest for 7 years.

(7) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 3% simple interest for 7 years.

(8) How much loan did Donald borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8125 to clear it?

(9) Find the amount to be paid if Thomas borrowed a sum of $5800 at 7% simple interest for 8 years.

(10) Calculate the amount due after 9 years if Charles borrowed a sum of $5900 at a rate of 3% simple interest.