Simple Interest
Math MCQs

Question :    Robert took a loan of $4200 at the rate of 7% simple interest per annum. If he paid an amount of $7140 to clear the loan, then find the time period of the loan.

Correct Answer  10

Solution & Explanation

Solution

Given,

Principal (P) = $4200

Rate of Simple Interest (R) = 7% per annum

Amount (A) = $7140

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 = $7140 – $4200 = $2940

Thus, Simple Interest = $2940

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 × 2940}/_{4200 × 7}

= ²⁹⁴⁰⁰⁰/₂₉₄₀₀

= 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) = $4200

Rate of Simple Interest (R) = 7% per annum

Simple Interest = $2940 (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 = 7% of Principal

= 7% of $4200

= ⁷/₁₀₀ × 4200

= ^{7 × 4200}/₁₀₀

= ²⁹⁴⁰⁰/₁₀₀ = 294

Thus, simple Interest for 1 year = $294

Now,

∵ If the simple Interest is $294, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₂₉₄ years

∴ If the simple Interest is $2940, then the time = ¹/₂₉₄ × 2940 years

= ^{1 × 2940}/₂₉₄ years

= ²⁹⁴⁰/₂₉₄ = 10 years

Thus, time (T) = 10 years Answer

Similar Questions

(1) Mary took a loan of $4100 at the rate of 10% simple interest per annum. If he paid an amount of $6970 to clear the loan, then find the time period of the loan.

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

(3) Find the amount to be paid if Michael borrowed a sum of $5300 at 2% simple interest for 7 years.

(4) How much loan did Michael borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5830 to clear it?

(5) What amount does Patricia have to pay after 5 years if he takes a loan of $3150 at 5% simple interest?

(6) What amount will be due after 2 years if James borrowed a sum of $3000 at a 8% simple interest?

(7) Andrew had to pay $5376 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(8) Calculate the amount due if Susan borrowed a sum of $3650 at 2% simple interest for 4 years.

(9) How much loan did Laura borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9812.5 to clear it?

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