Simple Interest
Math MCQs

Question :    Jessica took a loan of $5500 at the rate of 7% simple interest per annum. If he paid an amount of $8195 to clear the loan, then find the time period of the loan.

Correct Answer  7

Solution & Explanation

Solution

Given,

Principal (P) = $5500

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

Amount (A) = $8195

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 = $8195 – $5500 = $2695

Thus, Simple Interest = $2695

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 × 2695}/_{5500 × 7}

= ²⁶⁹⁵⁰⁰/₃₈₅₀₀

= 7 years (using formula)

Thus, Time (T) = 7 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) = 7% per annum

Simple Interest = $2695 (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 $5500

= ⁷/₁₀₀ × 5500

= ^{7 × 5500}/₁₀₀

= ³⁸⁵⁰⁰/₁₀₀ = 385

Thus, simple Interest for 1 year = $385

Now,

∵ If the simple Interest is $385, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₃₈₅ years

∴ If the simple Interest is $2695, then the time = ¹/₃₈₅ × 2695 years

= ^{1 × 2695}/₃₈₅ years

= ²⁶⁹⁵/₃₈₅ = 7 years

Thus, time (T) = 7 years Answer

Similar Questions

(1) How much loan did Matthew borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7130 to clear it?

(2) Calculate the amount due after 9 years if Jennifer borrowed a sum of $5250 at a rate of 3% simple interest.

(3) Find the amount to be paid if Karen borrowed a sum of $5950 at 9% simple interest for 7 years.

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

(5) In how much time a principal of $3200 will amount to $4000 at a simple interest of 5% per annum?

(6) How much loan did Barbara borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6382.5 to clear it?

(7) Sandra took a loan of $6900 at the rate of 7% simple interest per annum. If he paid an amount of $11730 to clear the loan, then find the time period of the loan.

(8) Find the amount to be paid if John borrowed a sum of $5200 at 9% simple interest for 7 years.

(9) Calculate the amount due if Thomas borrowed a sum of $3800 at 9% simple interest for 3 years.

(10) Find the amount to be paid if Joseph borrowed a sum of $5700 at 4% simple interest for 8 years.