Simple Interest
Math MCQs

Question :    Jessica took a loan of $5500 at the rate of 6% simple interest per annum. If he paid an amount of $8800 to clear the loan, then find the time period of the loan.

Correct Answer  10

Solution & Explanation

Solution

Given,

Principal (P) = $5500

Rate of Simple Interest (R) = 6% per annum

Amount (A) = $8800

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 = $8800 – $5500 = $3300

Thus, Simple Interest = $3300

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 × 3300}/_{5500 × 6}

= ³³⁰⁰⁰⁰/₃₃₀₀₀

= 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) = $5500

Rate of Simple Interest (R) = 6% per annum

Simple Interest = $3300 (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 = 6% of Principal

= 6% of $5500

= ⁶/₁₀₀ × 5500

= ^{6 × 5500}/₁₀₀

= ³³⁰⁰⁰/₁₀₀ = 330

Thus, simple Interest for 1 year = $330

Now,

∵ If the simple Interest is $330, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₃₃₀ years

∴ If the simple Interest is $3300, then the time = ¹/₃₃₀ × 3300 years

= ^{1 × 3300}/₃₃₀ years

= ³³⁰⁰/₃₃₀ = 10 years

Thus, time (T) = 10 years Answer

Similar Questions

(1) What amount does Patricia have to pay after 6 years if he takes a loan of $3150 at 7% simple interest?

(2) Thomas took a loan of $5600 at the rate of 6% simple interest per annum. If he paid an amount of $8288 to clear the loan, then find the time period of the loan.

(3) If Nancy paid $4648 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(4) In how much time a principal of $3000 will amount to $3240 at a simple interest of 2% per annum?

(5) Calculate the amount due after 10 years if Charles borrowed a sum of $5900 at a rate of 7% simple interest.

(6) Calculate the amount due after 9 years if Elizabeth borrowed a sum of $5450 at a rate of 8% simple interest.

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

(8) What amount will be due after 2 years if Daniel borrowed a sum of $3550 at a 7% simple interest?

(9) If Patricia borrowed $3150 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.

(10) Sandra took a loan of $6900 at the rate of 8% simple interest per annum. If he paid an amount of $12420 to clear the loan, then find the time period of the loan.