Simple Interest
Math MCQs

Question :    How much loan did Margaret borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7302.5 to clear it?

Correct Answer  $6350

Solution & Explanation

Solution

Given,

Amount (A) = $7302.5

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

$7302.5 = P (1 + 3% × 5)

⇒ $7302.5 = P (1 + ³/₁₀₀ × 5)

⇒ $7302.5 = P (1 + ^{3 × 5}/₁₀₀)

⇒ $7302.5 = P (1 + ¹⁵/₁₀₀)

⇒ $7302.5 = P (^{100 + 15}/₁₀₀)

⇒ $7302.5 = P × ¹¹⁵/₁₀₀

⇒ P × ¹¹⁵/₁₀₀ = $7302.5

⇒ P = ^7302.5/_¹¹⁵/100

⇒ P = 7302.5 × ¹⁰⁰/₁₁₅

⇒ P = ^{7302.5 × 100}/₁₁₅

⇒ P = ⁷³⁰²⁵⁰/₁₁₅

⇒ P = $6350

Thus, the sum borrowed (P) = $6350 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 7302.5, then the Principal = ¹⁰⁰/₁₁₅ × 7302.5

= ^{100 × 7302.5}/₁₁₅

= ⁷³⁰²⁵⁰/₁₁₅

= 6350

Thus, Principal = $6350

Thus, the sum borrowed = $6350 Answer

Similar Questions

(1) What amount does Charles have to pay after 5 years if he takes a loan of $3900 at 10% simple interest?

(2) Find the amount to be paid if Susan borrowed a sum of $5650 at 4% simple interest for 8 years.

(3) What amount does John have to pay after 5 years if he takes a loan of $3200 at 6% simple interest?

(4) Matthew took a loan of $6400 at the rate of 8% simple interest per annum. If he paid an amount of $10496 to clear the loan, then find the time period of the loan.

(5) Mary had to pay $3324.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(6) How much loan did Jeffrey borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9750 to clear it?

(7) What amount will be due after 2 years if Andrew borrowed a sum of $3900 at a 7% simple interest?

(8) What amount does Linda have to pay after 5 years if he takes a loan of $3350 at 7% simple interest?

(9) What amount does Charles have to pay after 5 years if he takes a loan of $3900 at 3% simple interest?

(10) Karen took a loan of $5900 at the rate of 10% simple interest per annum. If he paid an amount of $11800 to clear the loan, then find the time period of the loan.