Simple Interest
MCQs Math

Question:     Susan took a loan of $5300 at the rate of 8% simple interest per annum. If he paid an amount of $9540 to clear the loan, then find the time period of the loan.

Correct Answer  10

Solution And Explanation

Solution

Given,

Principal (P) = $5300

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

Amount (A) = $9540

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 = $9540 – $5300 = $4240

Thus, Simple Interest = $4240

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 × 4240}/_{5300 × 8}

= ⁴²⁴⁰⁰⁰/₄₂₄₀₀

= 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) = $5300

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

Simple Interest = $4240 (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 $5300

= ⁸/₁₀₀ × 5300

= ^{8 × 5300}/₁₀₀

= ⁴²⁴⁰⁰/₁₀₀ = 424

Thus, simple Interest for 1 year = $424

Now,

∵ If the simple Interest is $424, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₄₂₄ years

∴ If the simple Interest is $4240, then the time = ¹/₄₂₄ × 4240 years

= ^{1 × 4240}/₄₂₄ years

= ⁴²⁴⁰/₄₂₄ = 10 years

Thus, time (T) = 10 years Answer

Similar Questions

(1) How much loan did Barbara borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6105 to clear it?

(2) Find the amount to be paid if Karen borrowed a sum of $5950 at 5% simple interest for 8 years.

(3) Calculate the amount due if Karen borrowed a sum of $3950 at 3% simple interest for 4 years.

(4) How much loan did Carol borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8460 to clear it?

(5) Calculate the amount due if Michael borrowed a sum of $3300 at 6% simple interest for 3 years.

(6) Find the amount to be paid if Joseph borrowed a sum of $5700 at 10% simple interest for 7 years.

(7) Find the amount to be paid if Charles borrowed a sum of $5900 at 5% simple interest for 8 years.

(8) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 6% simple interest for 7 years.

(9) What amount does James have to pay after 5 years if he takes a loan of $3000 at 4% simple interest?

(10) Donald took a loan of $7000 at the rate of 6% simple interest per annum. If he paid an amount of $10360 to clear the loan, then find the time period of the loan.