Simple Interest
Math MCQs

Question :    Daniel took a loan of $6200 at the rate of 8% simple interest per annum. If he paid an amount of $10664 to clear the loan, then find the time period of the loan.

Correct Answer  9

Solution & Explanation

Solution

Given,

Principal (P) = $6200

Rate of Simple Interest (R) = 8% per annum

Amount (A) = $10664

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 = $10664 – $6200 = $4464

Thus, Simple Interest = $4464

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 × 4464}/_{6200 × 8}

= ⁴⁴⁶⁴⁰⁰/₄₉₆₀₀

= 9 years (using formula)

Thus, Time (T) = 9 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) = $6200

Rate of Simple Interest (R) = 8% per annum

Simple Interest = $4464 (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 = 8% of Principal

= 8% of $6200

= ⁸/₁₀₀ × 6200

= ^{8 × 6200}/₁₀₀

= ⁴⁹⁶⁰⁰/₁₀₀ = 496

Thus, simple Interest for 1 year = $496

Now,

∵ If the simple Interest is $496, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₄₉₆ years

∴ If the simple Interest is $4464, then the time = ¹/₄₉₆ × 4464 years

= ^{1 × 4464}/₄₉₆ years

= ⁴⁴⁶⁴/₄₉₆ = 9 years

Thus, time (T) = 9 years Answer

Similar Questions

(1) If Jennifer paid $3900 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(2) Calculate the amount due after 10 years if Patricia borrowed a sum of $5150 at a rate of 10% simple interest.

(3) How much loan did Michelle borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7645 to clear it?

(4) If Karen paid $4740 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(5) Christopher took a loan of $6000 at the rate of 9% simple interest per annum. If he paid an amount of $9780 to clear the loan, then find the time period of the loan.

(6) Find the amount to be paid if John borrowed a sum of $5200 at 4% simple interest for 8 years.

(7) Karen took a loan of $5900 at the rate of 10% simple interest per annum. If he paid an amount of $10620 to clear the loan, then find the time period of the loan.

(8) Lisa took a loan of $6100 at the rate of 7% simple interest per annum. If he paid an amount of $10370 to clear the loan, then find the time period of the loan.

(9) If William borrowed $3500 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.

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