Simple Interest
MCQs Math

Question:     Patricia took a loan of $4300 at the rate of 8% simple interest per annum. If he paid an amount of $6364 to clear the loan, then find the time period of the loan.

Correct Answer  6

Solution And Explanation

Solution

Given,

Principal (P) = $4300

Rate of Simple Interest (R) = 8% per annum

Amount (A) = $6364

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 = $6364 – $4300 = $2064

Thus, Simple Interest = $2064

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 × 2064}/_{4300 × 8}

= ²⁰⁶⁴⁰⁰/₃₄₄₀₀

= 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) = $4300

Rate of Simple Interest (R) = 8% per annum

Simple Interest = $2064 (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 = 8% of Principal

= 8% of $4300

= ⁸/₁₀₀ × 4300

= ^{8 × 4300}/₁₀₀

= ³⁴⁴⁰⁰/₁₀₀ = 344

Thus, simple Interest for 1 year = $344

Now,

∵ If the simple Interest is $344, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₃₄₄ years

∴ If the simple Interest is $2064, then the time = ¹/₃₄₄ × 2064 years

= ^{1 × 2064}/₃₄₄ years

= ²⁰⁶⁴/₃₄₄ = 6 years

Thus, time (T) = 6 years Answer

Similar Questions

(1) What amount does Michael have to pay after 5 years if he takes a loan of $3300 at 9% simple interest?

(2) In how much time a principal of $3150 will amount to $3433.5 at a simple interest of 3% per annum?

(3) Barbara took a loan of $5100 at the rate of 8% simple interest per annum. If he paid an amount of $9180 to clear the loan, then find the time period of the loan.

(4) Patricia took a loan of $4300 at the rate of 10% simple interest per annum. If he paid an amount of $6880 to clear the loan, then find the time period of the loan.

(5) If Michael paid $3828 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(6) How much loan did James borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $5750 to clear it?

(7) What amount will be due after 2 years if Joseph borrowed a sum of $3350 at a 4% simple interest?

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

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

(10) Calculate the amount due after 10 years if John borrowed a sum of $5200 at a rate of 10% simple interest.