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) Calculate the amount due after 10 years if Charles borrowed a sum of $5900 at a rate of 8% simple interest.

(2) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 6% simple interest?

(3) Charles took a loan of $5800 at the rate of 8% simple interest per annum. If he paid an amount of $9512 to clear the loan, then find the time period of the loan.

(4) Christopher took a loan of $6000 at the rate of 10% simple interest per annum. If he paid an amount of $10200 to clear the loan, then find the time period of the loan.

(5) Richard took a loan of $5200 at the rate of 10% simple interest per annum. If he paid an amount of $10400 to clear the loan, then find the time period of the loan.

(6) Calculate the amount due if John borrowed a sum of $3200 at 4% simple interest for 3 years.

(7) If James paid $3240 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(8) Betty took a loan of $6500 at the rate of 7% simple interest per annum. If he paid an amount of $10140 to clear the loan, then find the time period of the loan.

(9) Calculate the amount due if Karen borrowed a sum of $3950 at 5% simple interest for 4 years.

(10) What amount does Jessica have to pay after 6 years if he takes a loan of $3750 at 9% simple interest?