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 $9656 to clear the loan, then find the time period of the loan.

Correct Answer  6

Solution & Explanation

Solution

Given,

Principal (P) = $6800

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

Amount (A) = $9656

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 = $9656 – $6800 = $2856

Thus, Simple Interest = $2856

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 × 2856}/_{6800 × 7}

= ²⁸⁵⁶⁰⁰/₄₇₆₀₀

= 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) = $6800

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

Simple Interest = $2856 (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 $2856, then the time = ¹/₄₇₆ × 2856 years

= ^{1 × 2856}/₄₇₆ years

= ²⁸⁵⁶/₄₇₆ = 6 years

Thus, time (T) = 6 years Answer

Similar Questions

(1) Sarah took a loan of $5700 at the rate of 7% simple interest per annum. If he paid an amount of $8892 to clear the loan, then find the time period of the loan.

(2) Calculate the amount due if John borrowed a sum of $3200 at 7% simple interest for 3 years.

(3) Calculate the amount due if Barbara borrowed a sum of $3550 at 7% simple interest for 4 years.

(4) If Mark paid $5104 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(5) What amount will be due after 2 years if James borrowed a sum of $3000 at a 7% simple interest?

(6) Calculate the amount due if Mary borrowed a sum of $3050 at 9% simple interest for 3 years.

(7) What amount will be due after 2 years if Joshua borrowed a sum of $3950 at a 10% simple interest?

(8) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 4% simple interest for 7 years.

(9) Jennifer took a loan of $4500 at the rate of 10% simple interest per annum. If he paid an amount of $9000 to clear the loan, then find the time period of the loan.

(10) Charles took a loan of $5800 at the rate of 9% simple interest per annum. If he paid an amount of $8932 to clear the loan, then find the time period of the loan.