Simple Interest
Math MCQs

Question :    Patricia took a loan of $4300 at the rate of 7% simple interest per annum. If he paid an amount of $6407 to clear the loan, then find the time period of the loan.

Correct Answer  7

Solution & Explanation

Solution

Given,

Principal (P) = $4300

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

Amount (A) = $6407

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 = $6407 – $4300 = $2107

Thus, Simple Interest = $2107

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 × 2107}/_{4300 × 7}

= ²¹⁰⁷⁰⁰/₃₀₁₀₀

= 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) = $4300

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

Simple Interest = $2107 (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 $4300

= ⁷/₁₀₀ × 4300

= ^{7 × 4300}/₁₀₀

= ³⁰¹⁰⁰/₁₀₀ = 301

Thus, simple Interest for 1 year = $301

Now,

∵ If the simple Interest is $301, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₃₀₁ years

∴ If the simple Interest is $2107, then the time = ¹/₃₀₁ × 2107 years

= ^{1 × 2107}/₃₀₁ years

= ²¹⁰⁷/₃₀₁ = 7 years

Thus, time (T) = 7 years Answer

Similar Questions

(1) What amount does Christopher have to pay after 5 years if he takes a loan of $4000 at 7% simple interest?

(2) In how much time a principal of $3000 will amount to $3600 at a simple interest of 4% per annum?

(3) Find the amount to be paid if Robert borrowed a sum of $5100 at 7% simple interest for 7 years.

(4) What amount does William have to pay after 6 years if he takes a loan of $3500 at 2% simple interest?

(5) Calculate the amount due if James borrowed a sum of $3000 at 6% simple interest for 3 years.

(6) Charles took a loan of $5800 at the rate of 10% simple interest per annum. If he paid an amount of $10440 to clear the loan, then find the time period of the loan.

(7) Sandra took a loan of $6900 at the rate of 8% simple interest per annum. If he paid an amount of $10212 to clear the loan, then find the time period of the loan.

(8) Calculate the amount due if William borrowed a sum of $3500 at 3% simple interest for 4 years.

(9) If Michael paid $3696 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(10) Find the amount to be paid if Charles borrowed a sum of $5900 at 5% simple interest for 7 years.