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) Find the amount to be paid if Richard borrowed a sum of $5600 at 8% simple interest for 8 years.

(2) What amount does Mary have to pay after 6 years if he takes a loan of $3050 at 4% simple interest?

(3) Calculate the amount due after 10 years if Charles borrowed a sum of $5900 at a rate of 4% simple interest.

(4) What amount does Patricia have to pay after 6 years if he takes a loan of $3150 at 2% simple interest?

(5) How much loan did Nancy borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7072.5 to clear it?

(6) Find the amount to be paid if William borrowed a sum of $5500 at 4% simple interest for 8 years.

(7) Calculate the amount due after 9 years if Richard borrowed a sum of $5600 at a rate of 6% simple interest.

(8) Calculate the amount due if Linda borrowed a sum of $3350 at 10% simple interest for 4 years.

(9) Richard had to pay $3924 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(10) How much loan did Carol borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7755 to clear it?