Simple Interest
Math MCQs

Question :    If Sandra paid $5340 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

Correct Answer  $4450

Solution & Explanation

Solution

Given,

Amount (A) = $5340

Rate of Simple Interest (R) = 5%

Time (T) = 4 years

Thus, Principal (P) = ?

Method (1) Using Formula

Calculation of the Principal using forumula when Amount, Time and Rate of Simple Interest are given

Formula to find the Principal (P)

Amount (A) = Principal (P) + Principal (P) × Rate (R) × Time (T)

⇒ Amount (A) = Principal (P) [1 + Rate (R) × Time (T)]

⇒ A = P (1 + RT)

Using the formula to find the Amount (A), the fourth can be calculated if any three of A, P, R, and T are given

In the given question, we need to find the Principal (P)

Therefore, by substituting, Amount, Rate, and Time, in the formula A = P (1 + RT) we get

$5340 = P (1 + 5% × 4)

⇒ $5340 = P (1 + ⁵/₁₀₀ × 4)

⇒ $5340 = P (1 + ^{5 × 4}/₁₀₀)

⇒ $5340 = P (1 + ²⁰/₁₀₀)

⇒ $5340 = P (^{100 + 20}/₁₀₀)

⇒ $5340 = P × ¹²⁰/₁₀₀

⇒ P × ¹²⁰/₁₀₀ = $5340

⇒ P = ⁵³⁴⁰/_¹²⁰/100

⇒ P = 5340 × ¹⁰⁰/₁₂₀

⇒ P = ^{5340 × 100}/₁₂₀

⇒ P = ⁵³⁴⁰⁰⁰/₁₂₀

⇒ P = $4450

Thus, the sum borrowed (P) = $4450 Answer

Method (1) Using Unitary Method

Calculation of the Principal using unitary method when Amount, Time and Rate of Simple Interest are given

Calculation of the Simple Interest

Let, the principal = 100

Here, since rate of simple interest = 5% per annum

Thus, Interest = 5% of principal

⇒ Interest = 5% of 100 = 5

Thus, Simple Interest for 1 year = 5

Calculation of the Amount

Since, in the question, time = 4 years

So, we need to calculate the simple interest for the given time period, which is 4 years

Thus, Simple Interest for 4 years = 4 × Simple Interest for 1 year

= 4 × 5 = 20

Thus, simple interest for 4 years = 20

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 20 = 120

Calculation of the Principal

Now,

∵ If the Amount is 120, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₂₀

∴ If the Amount is 5340, then the Principal = ¹⁰⁰/₁₂₀ × 5340

= ^{100 × 5340}/₁₂₀

= ⁵³⁴⁰⁰⁰/₁₂₀

= 4450

Thus, Principal = $4450

Thus, the sum borrowed = $4450 Answer

Similar Questions

(1) Margaret took a loan of $6700 at the rate of 9% simple interest per annum. If he paid an amount of $10318 to clear the loan, then find the time period of the loan.

(2) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 4% simple interest for 7 years.

(3) Calculate the amount due if William borrowed a sum of $3500 at 6% simple interest for 4 years.

(4) What amount will be due after 2 years if Matthew borrowed a sum of $3600 at a 8% simple interest?

(5) How much loan did Margaret borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6985 to clear it?

(6) Calculate the amount due after 10 years if Mary borrowed a sum of $5050 at a rate of 8% simple interest.

(7) Nancy took a loan of $6300 at the rate of 6% simple interest per annum. If he paid an amount of $10080 to clear the loan, then find the time period of the loan.

(8) Mary took a loan of $4100 at the rate of 9% simple interest per annum. If he paid an amount of $7790 to clear the loan, then find the time period of the loan.

(9) What amount does John have to pay after 6 years if he takes a loan of $3200 at 9% simple interest?

(10) What amount does Sarah have to pay after 5 years if he takes a loan of $3850 at 4% simple interest?