Simple Interest
Math MCQs

Question :    Margaret took a loan of $6700 at the rate of 10% simple interest per annum. If he paid an amount of $11390 to clear the loan, then find the time period of the loan.

Correct Answer  7

Solution & Explanation

Solution

Given,

Principal (P) = $6700

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

Amount (A) = $11390

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 = $11390 – $6700 = $4690

Thus, Simple Interest = $4690

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 × 4690}/_{6700 × 10}

= ⁴⁶⁹⁰⁰⁰/₆₇₀₀₀

= 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) = $6700

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

Simple Interest = $4690 (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 $6700

= ¹⁰/₁₀₀ × 6700

= ^{10 × 6700}/₁₀₀

= ⁶⁷⁰⁰⁰/₁₀₀ = 670

Thus, simple Interest for 1 year = $670

Now,

∵ If the simple Interest is $670, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₆₇₀ years

∴ If the simple Interest is $4690, then the time = ¹/₆₇₀ × 4690 years

= ^{1 × 4690}/₆₇₀ years

= ⁴⁶⁹⁰/₆₇₀ = 7 years

Thus, time (T) = 7 years Answer

Similar Questions

(1) Calculate the amount due if David borrowed a sum of $3400 at 3% simple interest for 4 years.

(2) Calculate the amount due after 10 years if Robert borrowed a sum of $5100 at a rate of 8% simple interest.

(3) 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.

(4) Jennifer took a loan of $4500 at the rate of 8% simple interest per annum. If he paid an amount of $6660 to clear the loan, then find the time period of the loan.

(5) William took a loan of $5000 at the rate of 6% simple interest per annum. If he paid an amount of $7400 to clear the loan, then find the time period of the loan.

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

(7) Calculate the amount due after 9 years if Barbara borrowed a sum of $5550 at a rate of 3% simple interest.

(8) Calculate the amount due if David borrowed a sum of $3400 at 8% simple interest for 3 years.

(9) What amount does William have to pay after 5 years if he takes a loan of $3500 at 9% simple interest?

(10) Daniel took a loan of $6200 at the rate of 6% simple interest per annum. If he paid an amount of $8804 to clear the loan, then find the time period of the loan.