Simple Interest
Math MCQs

Question :    Richard took a loan of $5200 at the rate of 9% simple interest per annum. If he paid an amount of $8008 to clear the loan, then find the time period of the loan.

Correct Answer  6

Solution & Explanation

Solution

Given,

Principal (P) = $5200

Rate of Simple Interest (R) = 9% per annum

Amount (A) = $8008

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 = $8008 – $5200 = $2808

Thus, Simple Interest = $2808

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 × 2808}/_{5200 × 9}

= ²⁸⁰⁸⁰⁰/₄₆₈₀₀

= 6 years (using formula)

Thus, Time (T) = 6 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) = $5200

Rate of Simple Interest (R) = 9% per annum

Simple Interest = $2808 (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 = 9% of Principal

= 9% of $5200

= ⁹/₁₀₀ × 5200

= ^{9 × 5200}/₁₀₀

= ⁴⁶⁸⁰⁰/₁₀₀ = 468

Thus, simple Interest for 1 year = $468

Now,

∵ If the simple Interest is $468, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₄₆₈ years

∴ If the simple Interest is $2808, then the time = ¹/₄₆₈ × 2808 years

= ^{1 × 2808}/₄₆₈ years

= ²⁸⁰⁸/₄₆₈ = 6 years

Thus, time (T) = 6 years Answer

Similar Questions

(1) Calculate the amount due if Mary borrowed a sum of $3050 at 10% simple interest for 4 years.

(2) Calculate the amount due if Thomas borrowed a sum of $3800 at 2% simple interest for 4 years.

(3) Calculate the amount due if Susan borrowed a sum of $3650 at 7% simple interest for 3 years.

(4) What amount does William have to pay after 5 years if he takes a loan of $3500 at 7% simple interest?

(5) Christopher took a loan of $6000 at the rate of 9% simple interest per annum. If he paid an amount of $10320 to clear the loan, then find the time period of the loan.

(6) In how much time a principal of $3000 will amount to $3180 at a simple interest of 3% per annum?

(7) What amount will be due after 2 years if James borrowed a sum of $3000 at a 9% simple interest?

(8) If Lisa paid $4860 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(9) Calculate the amount due if Thomas borrowed a sum of $3800 at 4% simple interest for 4 years.

(10) Calculate the amount due after 10 years if David borrowed a sum of $5400 at a rate of 3% simple interest.