Simple Interest
Math MCQs

Question :    How much loan did Elizabeth borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6267.5 to clear it?

Correct Answer  $5450

Solution & Explanation

Solution

Given,

Amount (A) = $6267.5

Rate of Simple Interest (R) = 3%

Time (T) = 5 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

$6267.5 = P (1 + 3% × 5)

⇒ $6267.5 = P (1 + ³/₁₀₀ × 5)

⇒ $6267.5 = P (1 + ^{3 × 5}/₁₀₀)

⇒ $6267.5 = P (1 + ¹⁵/₁₀₀)

⇒ $6267.5 = P (^{100 + 15}/₁₀₀)

⇒ $6267.5 = P × ¹¹⁵/₁₀₀

⇒ P × ¹¹⁵/₁₀₀ = $6267.5

⇒ P = ^6267.5/_¹¹⁵/100

⇒ P = 6267.5 × ¹⁰⁰/₁₁₅

⇒ P = ^{6267.5 × 100}/₁₁₅

⇒ P = ⁶²⁶⁷⁵⁰/₁₁₅

⇒ P = $5450

Thus, the sum borrowed (P) = $5450 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 = 3% per annum

Thus, Interest = 3% of principal

⇒ Interest = 3% of 100 = 3

Thus, Simple Interest for 1 year = 3

Calculation of the Amount

Since, in the question, time = 5 years

So, we need to calculate the simple interest for the given time period, which is 5 years

Thus, Simple Interest for 5 years = 5 × Simple Interest for 1 year

= 5 × 3 = 15

Thus, simple interest for 5 years = 15

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 15 = 115

Calculation of the Principal

Now,

∵ If the Amount is 115, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₁₅

∴ If the Amount is 6267.5, then the Principal = ¹⁰⁰/₁₁₅ × 6267.5

= ^{100 × 6267.5}/₁₁₅

= ⁶²⁶⁷⁵⁰/₁₁₅

= 5450

Thus, Principal = $5450

Thus, the sum borrowed = $5450 Answer

Similar Questions

(1) John took a loan of $4400 at the rate of 6% simple interest per annum. If he paid an amount of $5984 to clear the loan, then find the time period of the loan.

(2) Calculate the amount due if David borrowed a sum of $3400 at 6% simple interest for 3 years.

(3) Calculate the amount due if Karen borrowed a sum of $3950 at 3% simple interest for 4 years.

(4) What amount will be due after 2 years if Joseph borrowed a sum of $3350 at a 8% simple interest?

(5) What amount does Karen have to pay after 5 years if he takes a loan of $3950 at 8% simple interest?

(6) Calculate the amount due if Christopher borrowed a sum of $4000 at 4% simple interest for 4 years.

(7) How much loan did Sarah borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6435 to clear it?

(8) Calculate the amount due if Patricia borrowed a sum of $3150 at 9% simple interest for 4 years.

(9) Find the amount to be paid if Karen borrowed a sum of $5950 at 10% simple interest for 7 years.

(10) Find the amount to be paid if Karen borrowed a sum of $5950 at 9% simple interest for 7 years.