Simple Interest
Math MCQs

Question :    Robert took a loan of $4200 at the rate of 10% simple interest per annum. If he paid an amount of $7980 to clear the loan, then find the time period of the loan.

Correct Answer  9

Solution & Explanation

Solution

Given,

Principal (P) = $4200

Rate of Simple Interest (R) = 10% per annum

Amount (A) = $7980

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 = $7980 – $4200 = $3780

Thus, Simple Interest = $3780

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 × 3780}/_{4200 × 10}

= ³⁷⁸⁰⁰⁰/₄₂₀₀₀

= 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) = $4200

Rate of Simple Interest (R) = 10% per annum

Simple Interest = $3780 (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 $4200

= ¹⁰/₁₀₀ × 4200

= ^{10 × 4200}/₁₀₀

= ⁴²⁰⁰⁰/₁₀₀ = 420

Thus, simple Interest for 1 year = $420

Now,

∵ If the simple Interest is $420, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₄₂₀ years

∴ If the simple Interest is $3780, then the time = ¹/₄₂₀ × 3780 years

= ^{1 × 3780}/₄₂₀ years

= ³⁷⁸⁰/₄₂₀ = 9 years

Thus, time (T) = 9 years Answer

Similar Questions

(1) Sandra took a loan of $6900 at the rate of 10% simple interest per annum. If he paid an amount of $11040 to clear the loan, then find the time period of the loan.

(2) Thomas took a loan of $5600 at the rate of 9% simple interest per annum. If he paid an amount of $9128 to clear the loan, then find the time period of the loan.

(3) Calculate the amount due after 9 years if Michael borrowed a sum of $5300 at a rate of 7% simple interest.

(4) Ashley had to pay $4823 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(5) Betty had to pay $4505 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(6) Calculate the amount due if Joseph borrowed a sum of $3700 at 3% simple interest for 3 years.

(7) How much loan did Susan borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6780 to clear it?

(8) Calculate the amount due after 9 years if Joseph borrowed a sum of $5700 at a rate of 4% simple interest.

(9) Calculate the amount due if Robert borrowed a sum of $3100 at 8% simple interest for 4 years.

(10) Find the amount to be paid if Barbara borrowed a sum of $5550 at 6% simple interest for 8 years.