Simple Interest
Math MCQs

Question :    Mary took a loan of $4100 at the rate of 7% simple interest per annum. If he paid an amount of $5822 to clear the loan, then find the time period of the loan.

Correct Answer  6

Solution & Explanation

Solution

Given,

Principal (P) = $4100

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

Amount (A) = $5822

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 = $5822 – $4100 = $1722

Thus, Simple Interest = $1722

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 × 1722}/_{4100 × 7}

= ¹⁷²²⁰⁰/₂₈₇₀₀

= 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) = $4100

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

Simple Interest = $1722 (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 $4100

= ⁷/₁₀₀ × 4100

= ^{7 × 4100}/₁₀₀

= ²⁸⁷⁰⁰/₁₀₀ = 287

Thus, simple Interest for 1 year = $287

Now,

∵ If the simple Interest is $287, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₂₈₇ years

∴ If the simple Interest is $1722, then the time = ¹/₂₈₇ × 1722 years

= ^{1 × 1722}/₂₈₇ years

= ¹⁷²²/₂₈₇ = 6 years

Thus, time (T) = 6 years Answer

Similar Questions

(1) Find the amount to be paid if Christopher borrowed a sum of $6000 at 9% simple interest for 8 years.

(2) Calculate the amount due after 9 years if Sarah borrowed a sum of $5850 at a rate of 3% simple interest.

(3) Find the amount to be paid if Michael borrowed a sum of $5300 at 3% simple interest for 8 years.

(4) David took a loan of $4800 at the rate of 10% simple interest per annum. If he paid an amount of $9600 to clear the loan, then find the time period of the loan.

(5) Calculate the amount due if Robert borrowed a sum of $3100 at 7% simple interest for 3 years.

(6) How much loan did Christopher borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6900 to clear it?

(7) Lisa took a loan of $6100 at the rate of 6% simple interest per annum. If he paid an amount of $9760 to clear the loan, then find the time period of the loan.

(8) Calculate the amount due after 9 years if Charles borrowed a sum of $5900 at a rate of 6% simple interest.

(9) If Margaret paid $5220 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(10) Find the amount to be paid if Richard borrowed a sum of $5600 at 4% simple interest for 8 years.