Simple Interest
Math MCQs

Question :    William took a loan of $5000 at the rate of 9% simple interest per annum. If he paid an amount of $9500 to clear the loan, then find the time period of the loan.

Correct Answer  10

Solution & Explanation

Solution

Given,

Principal (P) = $5000

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

Amount (A) = $9500

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 = $9500 – $5000 = $4500

Thus, Simple Interest = $4500

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 × 4500}/_{5000 × 9}

= ⁴⁵⁰⁰⁰⁰/₄₅₀₀₀

= 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) = $5000

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

Simple Interest = $4500 (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 $5000

= ⁹/₁₀₀ × 5000

= ^{9 × 5000}/₁₀₀

= ⁴⁵⁰⁰⁰/₁₀₀ = 450

Thus, simple Interest for 1 year = $450

Now,

∵ If the simple Interest is $450, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₄₅₀ years

∴ If the simple Interest is $4500, then the time = ¹/₄₅₀ × 4500 years

= ^{1 × 4500}/₄₅₀ years

= ⁴⁵⁰⁰/₄₅₀ = 10 years

Thus, time (T) = 10 years Answer

Similar Questions

(1) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 2% simple interest for 7 years.

(2) How much loan did Mark borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7040 to clear it?

(3) If Mark paid $5280 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(4) What amount does Joseph have to pay after 5 years if he takes a loan of $3700 at 6% simple interest?

(5) If Joshua paid $5880 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(6) Donald took a loan of $7000 at the rate of 7% simple interest per annum. If he paid an amount of $11900 to clear the loan, then find the time period of the loan.

(7) What amount does Karen have to pay after 5 years if he takes a loan of $3950 at 4% simple interest?

(8) Find the amount to be paid if Sarah borrowed a sum of $5850 at 10% simple interest for 7 years.

(9) Lisa took a loan of $6100 at the rate of 6% simple interest per annum. If he paid an amount of $9028 to clear the loan, then find the time period of the loan.

(10) Margaret took a loan of $6700 at the rate of 10% simple interest per annum. If he paid an amount of $12060 to clear the loan, then find the time period of the loan.