Simple Interest
Math MCQs

Question :    Thomas took a loan of $5600 at the rate of 10% simple interest per annum. If he paid an amount of $11200 to clear the loan, then find the time period of the loan.

Correct Answer  10

Solution & Explanation

Solution

Given,

Principal (P) = $5600

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

Amount (A) = $11200

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 = $11200 – $5600 = $5600

Thus, Simple Interest = $5600

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 × 5600}/_{5600 × 10}

= ⁵⁶⁰⁰⁰⁰/₅₆₀₀₀

= 10 years (using formula)

Thus, Time (T) = 10 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) = $5600

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

Simple Interest = $5600 (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 $5600

= ¹⁰/₁₀₀ × 5600

= ^{10 × 5600}/₁₀₀

= ⁵⁶⁰⁰⁰/₁₀₀ = 560

Thus, simple Interest for 1 year = $560

Now,

∵ If the simple Interest is $560, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₅₆₀ years

∴ If the simple Interest is $5600, then the time = ¹/₅₆₀ × 5600 years

= ^{1 × 5600}/₅₆₀ years

= ⁵⁶⁰⁰/₅₆₀ = 10 years

Thus, time (T) = 10 years Answer

Similar Questions

(1) Patricia took a loan of $4300 at the rate of 8% simple interest per annum. If he paid an amount of $7396 to clear the loan, then find the time period of the loan.

(2) If Michael paid $3564 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(3) Calculate the amount due if Linda borrowed a sum of $3350 at 6% simple interest for 4 years.

(4) Calculate the amount due after 9 years if Mary borrowed a sum of $5050 at a rate of 3% simple interest.

(5) Calculate the amount due if Patricia borrowed a sum of $3150 at 3% simple interest for 4 years.

(6) Calculate the amount due after 10 years if Robert borrowed a sum of $5100 at a rate of 6% simple interest.

(7) What amount does Jessica have to pay after 6 years if he takes a loan of $3750 at 9% simple interest?

(8) Find the amount to be paid if William borrowed a sum of $5500 at 8% simple interest for 7 years.

(9) Mark took a loan of $6800 at the rate of 7% simple interest per annum. If he paid an amount of $10608 to clear the loan, then find the time period of the loan.

(10) If Kimberly paid $5580 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.