Simple Interest
Math MCQs

Question :    Mark took a loan of $6800 at the rate of 7% simple interest per annum. If he paid an amount of $10132 to clear the loan, then find the time period of the loan.

Correct Answer  7

Solution & Explanation

Solution

Given,

Principal (P) = $6800

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

Amount (A) = $10132

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 = $10132 – $6800 = $3332

Thus, Simple Interest = $3332

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 × 3332}/_{6800 × 7}

= ³³³²⁰⁰/₄₇₆₀₀

= 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) = $6800

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

Simple Interest = $3332 (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 $6800

= ⁷/₁₀₀ × 6800

= ^{7 × 6800}/₁₀₀

= ⁴⁷⁶⁰⁰/₁₀₀ = 476

Thus, simple Interest for 1 year = $476

Now,

∵ If the simple Interest is $476, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₄₇₆ years

∴ If the simple Interest is $3332, then the time = ¹/₄₇₆ × 3332 years

= ^{1 × 3332}/₄₇₆ years

= ³³³²/₄₇₆ = 7 years

Thus, time (T) = 7 years Answer

Similar Questions

(1) Find the amount to be paid if Thomas borrowed a sum of $5800 at 3% simple interest for 8 years.

(2) If Robert paid $3472 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(3) William took a loan of $5000 at the rate of 10% simple interest per annum. If he paid an amount of $8500 to clear the loan, then find the time period of the loan.

(4) Find the amount to be paid if Richard borrowed a sum of $5600 at 3% simple interest for 7 years.

(5) In how much time a principal of $3050 will amount to $3812.5 at a simple interest of 5% per annum?

(6) Calculate the amount due if Jennifer borrowed a sum of $3250 at 9% simple interest for 4 years.

(7) Donald took a loan of $7000 at the rate of 7% simple interest per annum. If he paid an amount of $10430 to clear the loan, then find the time period of the loan.

(8) Calculate the amount due after 9 years if Karen borrowed a sum of $5950 at a rate of 5% simple interest.

(9) What amount will be due after 2 years if Joshua borrowed a sum of $3950 at a 8% simple interest?

(10) Jennifer took a loan of $4500 at the rate of 10% simple interest per annum. If he paid an amount of $8100 to clear the loan, then find the time period of the loan.