Simple Interest
Math MCQs

Question :    Sandra took a loan of $6900 at the rate of 10% simple interest per annum. If he paid an amount of $11040 to clear the loan, then find the time period of the loan.

Correct Answer  6

Solution & Explanation

Solution

Given,

Principal (P) = $6900

Rate of Simple Interest (R) = 10% per annum

Amount (A) = $11040

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 = $11040 – $6900 = $4140

Thus, Simple Interest = $4140

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 × 4140}/_{6900 × 10}

= ⁴¹⁴⁰⁰⁰/₆₉₀₀₀

= 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) = $6900

Rate of Simple Interest (R) = 10% per annum

Simple Interest = $4140 (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 = 10% of Principal

= 10% of $6900

= ¹⁰/₁₀₀ × 6900

= ^{10 × 6900}/₁₀₀

= ⁶⁹⁰⁰⁰/₁₀₀ = 690

Thus, simple Interest for 1 year = $690

Now,

∵ If the simple Interest is $690, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₆₉₀ years

∴ If the simple Interest is $4140, then the time = ¹/₆₉₀ × 4140 years

= ^{1 × 4140}/₆₉₀ years

= ⁴¹⁴⁰/₆₉₀ = 6 years

Thus, time (T) = 6 years Answer

Similar Questions

(1) David took a loan of $4800 at the rate of 10% simple interest per annum. If he paid an amount of $8640 to clear the loan, then find the time period of the loan.

(2) Donald took a loan of $7000 at the rate of 9% simple interest per annum. If he paid an amount of $13300 to clear the loan, then find the time period of the loan.

(3) Sarah took a loan of $5700 at the rate of 10% simple interest per annum. If he paid an amount of $10260 to clear the loan, then find the time period of the loan.

(4) What amount will be due after 2 years if Thomas borrowed a sum of $3400 at a 4% simple interest?

(5) Find the amount to be paid if James borrowed a sum of $5000 at 6% simple interest for 7 years.

(6) Find the amount to be paid if Linda borrowed a sum of $5350 at 2% simple interest for 7 years.

(7) Susan took a loan of $5300 at the rate of 9% simple interest per annum. If he paid an amount of $8639 to clear the loan, then find the time period of the loan.

(8) Calculate the amount due after 9 years if Sarah borrowed a sum of $5850 at a rate of 10% simple interest.

(9) How much loan did Sandra borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7740 to clear it?

(10) If Emily paid $5320 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.