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 $7052 to clear the loan, then find the time period of the loan.

Correct Answer  8

Solution And Explanation

Solution

Given,

Principal (P) = $4300

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

Amount (A) = $7052

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 = $7052 – $4300 = $2752

Thus, Simple Interest = $2752

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 × 2752}/_{4300 × 8}

= ²⁷⁵²⁰⁰/₃₄₄₀₀

= 8 years (using formula)

Thus, Time (T) = 8 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 = $2752 (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 $2752, then the time = ¹/₃₄₄ × 2752 years

= ^{1 × 2752}/₃₄₄ years

= ²⁷⁵²/₃₄₄ = 8 years

Thus, time (T) = 8 years Answer

Similar Questions

(1) How much loan did Cynthia borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8745 to clear it?

(2) What amount does Richard have to pay after 6 years if he takes a loan of $3600 at 9% simple interest?

(3) In how much time a principal of $3150 will amount to $3402 at a simple interest of 4% per annum?

(4) Margaret took a loan of $6700 at the rate of 8% simple interest per annum. If he paid an amount of $11524 to clear the loan, then find the time period of the loan.

(5) If Jennifer paid $3900 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(6) Calculate the amount due if Michael borrowed a sum of $3300 at 9% simple interest for 4 years.

(7) Calculate the amount due if Robert borrowed a sum of $3100 at 9% simple interest for 4 years.

(8) Jennifer took a loan of $4500 at the rate of 9% simple interest per annum. If he paid an amount of $6930 to clear the loan, then find the time period of the loan.

(9) In how much time a principal of $3200 will amount to $3680 at a simple interest of 3% per annum?

(10) What amount does Michael have to pay after 5 years if he takes a loan of $3300 at 2% simple interest?