Simple Interest
Math MCQs

Question :    Patricia took a loan of $4300 at the rate of 6% simple interest per annum. If he paid an amount of $5848 to clear the loan, then find the time period of the loan.

Correct Answer  6

Solution & Explanation

Solution

Given,

Principal (P) = $4300

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

Amount (A) = $5848

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 = $5848 – $4300 = $1548

Thus, Simple Interest = $1548

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 × 1548}/_{4300 × 6}

= ¹⁵⁴⁸⁰⁰/₂₅₈₀₀

= 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) = 6% per annum

Simple Interest = $1548 (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 $4300

= ⁶/₁₀₀ × 4300

= ^{6 × 4300}/₁₀₀

= ²⁵⁸⁰⁰/₁₀₀ = 258

Thus, simple Interest for 1 year = $258

Now,

∵ If the simple Interest is $258, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₂₅₈ years

∴ If the simple Interest is $1548, then the time = ¹/₂₅₈ × 1548 years

= ^{1 × 1548}/₂₅₈ years

= ¹⁵⁴⁸/₂₅₈ = 6 years

Thus, time (T) = 6 years Answer

Similar Questions

(1) Patricia took a loan of $4300 at the rate of 8% simple interest per annum. If he paid an amount of $7396 to clear the loan, then find the time period of the loan.

(2) What amount does Thomas have to pay after 6 years if he takes a loan of $3800 at 8% simple interest?

(3) Calculate the amount due after 9 years if Joseph borrowed a sum of $5700 at a rate of 10% simple interest.

(4) Calculate the amount due after 10 years if Elizabeth borrowed a sum of $5450 at a rate of 9% simple interest.

(5) William took a loan of $5000 at the rate of 6% simple interest per annum. If he paid an amount of $7100 to clear the loan, then find the time period of the loan.

(6) Calculate the amount due after 10 years if William borrowed a sum of $5500 at a rate of 4% simple interest.

(7) Find the amount to be paid if David borrowed a sum of $5400 at 5% simple interest for 8 years.

(8) Jennifer took a loan of $4500 at the rate of 7% simple interest per annum. If he paid an amount of $7650 to clear the loan, then find the time period of the loan.

(9) How much loan did Stephanie borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8305 to clear it?

(10) If Ashley paid $4914 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.