Simple Interest
Math MCQs

Question :    Lisa took a loan of $6100 at the rate of 9% simple interest per annum. If he paid an amount of $11041 to clear the loan, then find the time period of the loan.

Correct Answer  9

Solution & Explanation

Solution

Given,

Principal (P) = $6100

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

Amount (A) = $11041

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 = $11041 – $6100 = $4941

Thus, Simple Interest = $4941

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 × 4941}/_{6100 × 9}

= ⁴⁹⁴¹⁰⁰/₅₄₉₀₀

= 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) = $6100

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

Simple Interest = $4941 (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 $6100

= ⁹/₁₀₀ × 6100

= ^{9 × 6100}/₁₀₀

= ⁵⁴⁹⁰⁰/₁₀₀ = 549

Thus, simple Interest for 1 year = $549

Now,

∵ If the simple Interest is $549, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₅₄₉ years

∴ If the simple Interest is $4941, then the time = ¹/₅₄₉ × 4941 years

= ^{1 × 4941}/₅₄₉ years

= ⁴⁹⁴¹/₅₄₉ = 9 years

Thus, time (T) = 9 years Answer

Similar Questions

(1) Sandra took a loan of $6900 at the rate of 8% simple interest per annum. If he paid an amount of $11868 to clear the loan, then find the time period of the loan.

(2) What amount does Mary have to pay after 5 years if he takes a loan of $3050 at 3% simple interest?

(3) Mark took a loan of $6800 at the rate of 9% simple interest per annum. If he paid an amount of $10472 to clear the loan, then find the time period of the loan.

(4) Calculate the amount due if David borrowed a sum of $3400 at 10% simple interest for 4 years.

(5) Sarah took a loan of $5700 at the rate of 7% simple interest per annum. If he paid an amount of $9690 to clear the loan, then find the time period of the loan.

(6) Calculate the amount due after 9 years if Jessica borrowed a sum of $5750 at a rate of 6% simple interest.

(7) What amount will be due after 2 years if William borrowed a sum of $3250 at a 10% simple interest?

(8) Joseph took a loan of $5400 at the rate of 6% simple interest per annum. If he paid an amount of $8316 to clear the loan, then find the time period of the loan.

(9) Calculate the amount due after 10 years if Christopher borrowed a sum of $6000 at a rate of 8% simple interest.

(10) What amount does David have to pay after 5 years if he takes a loan of $3400 at 6% simple interest?