Simple Interest
Math MCQs

Question :    Joseph took a loan of $5400 at the rate of 10% simple interest per annum. If he paid an amount of $10260 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) = 10% per annum

Amount (A) = $10260

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 = $10260 – $5400 = $4860

Thus, Simple Interest = $4860

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 × 4860}/_{5400 × 10}

= ⁴⁸⁶⁰⁰⁰/₅₄₀₀₀

= 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) = 10% per annum

Simple Interest = $4860 (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 = 10% of Principal

= 10% of $5400

= ¹⁰/₁₀₀ × 5400

= ^{10 × 5400}/₁₀₀

= ⁵⁴⁰⁰⁰/₁₀₀ = 540

Thus, simple Interest for 1 year = $540

Now,

∵ If the simple Interest is $540, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₅₄₀ years

∴ If the simple Interest is $4860, then the time = ¹/₅₄₀ × 4860 years

= ^{1 × 4860}/₅₄₀ years

= ⁴⁸⁶⁰/₅₄₀ = 9 years

Thus, time (T) = 9 years Answer

Similar Questions

(1) Calculate the amount due if Charles borrowed a sum of $3900 at 5% simple interest for 3 years.

(2) Find the amount to be paid if Patricia borrowed a sum of $5150 at 9% simple interest for 8 years.

(3) Joseph had to pay $4144 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(4) How much loan did Paul borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7370 to clear it?

(5) William took a loan of $5000 at the rate of 7% simple interest per annum. If he paid an amount of $7800 to clear the loan, then find the time period of the loan.

(6) Calculate the amount due after 9 years if Linda borrowed a sum of $5350 at a rate of 9% simple interest.

(7) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 7% simple interest for 8 years.

(8) Calculate the amount due if Barbara borrowed a sum of $3550 at 9% simple interest for 3 years.

(9) Find the amount to be paid if Thomas borrowed a sum of $5800 at 10% simple interest for 8 years.

(10) Mark took a loan of $6800 at the rate of 8% simple interest per annum. If he paid an amount of $11152 to clear the loan, then find the time period of the loan.