Simple Interest
Math MCQs

Question :    John took a loan of $4400 at the rate of 9% simple interest per annum. If he paid an amount of $7568 to clear the loan, then find the time period of the loan.

Correct Answer  8

Solution & Explanation

Solution

Given,

Principal (P) = $4400

Rate of Simple Interest (R) = 9% per annum

Amount (A) = $7568

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 = $7568 – $4400 = $3168

Thus, Simple Interest = $3168

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 × 3168}/_{4400 × 9}

= ³¹⁶⁸⁰⁰/₃₉₆₀₀

= 8 years (using formula)

Thus, Time (T) = 8 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) = $4400

Rate of Simple Interest (R) = 9% per annum

Simple Interest = $3168 (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 = 9% of Principal

= 9% of $4400

= ⁹/₁₀₀ × 4400

= ^{9 × 4400}/₁₀₀

= ³⁹⁶⁰⁰/₁₀₀ = 396

Thus, simple Interest for 1 year = $396

Now,

∵ If the simple Interest is $396, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₃₉₆ years

∴ If the simple Interest is $3168, then the time = ¹/₃₉₆ × 3168 years

= ^{1 × 3168}/₃₉₆ years

= ³¹⁶⁸/₃₉₆ = 8 years

Thus, time (T) = 8 years Answer

Similar Questions

(1) If William paid $3780 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(2) What amount will be due after 2 years if Kenneth borrowed a sum of $4000 at a 4% simple interest?

(3) What amount does Elizabeth have to pay after 5 years if he takes a loan of $3450 at 8% simple interest?

(4) What amount will be due after 2 years if Matthew borrowed a sum of $3600 at a 5% simple interest?

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

(6) If Susan paid $3942 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(7) Jessica took a loan of $5500 at the rate of 6% simple interest per annum. If he paid an amount of $8800 to clear the loan, then find the time period of the loan.

(8) Find the amount to be paid if Sarah borrowed a sum of $5850 at 5% simple interest for 7 years.

(9) Barbara took a loan of $5100 at the rate of 7% simple interest per annum. If he paid an amount of $7599 to clear the loan, then find the time period of the loan.

(10) Find the amount to be paid if James borrowed a sum of $5000 at 7% simple interest for 7 years.