Simple Interest
Math MCQs

Question :  ( 1 of 10 )  How much loan did Laura borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $9027.5 to clear it?

Correct Answer  $7850

Solution & Explanation

Solution

Given,

Amount (A) = $9027.5

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

$9027.5 = P (1 + 3% × 5)

⇒ $9027.5 = P (1 + ³/₁₀₀ × 5)

⇒ $9027.5 = P (1 + ^{3 × 5}/₁₀₀)

⇒ $9027.5 = P (1 + ¹⁵/₁₀₀)

⇒ $9027.5 = P (^{100 + 15}/₁₀₀)

⇒ $9027.5 = P × ¹¹⁵/₁₀₀

⇒ P × ¹¹⁵/₁₀₀ = $9027.5

⇒ P = ^9027.5/_¹¹⁵/100

⇒ P = 9027.5 × ¹⁰⁰/₁₁₅

⇒ P = ^{9027.5 × 100}/₁₁₅

⇒ P = ⁹⁰²⁷⁵⁰/₁₁₅

⇒ P = $7850

Thus, the sum borrowed (P) = $7850 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 9027.5, then the Principal = ¹⁰⁰/₁₁₅ × 9027.5

= ^{100 × 9027.5}/₁₁₅

= ⁹⁰²⁷⁵⁰/₁₁₅

= 7850

Thus, Principal = $7850

Thus, the sum borrowed = $7850 Answer

Similar Questions

(1) Donna had to pay $5577.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(2) Calculate the amount due if John borrowed a sum of $3200 at 8% simple interest for 4 years.

(3) Calculate the amount due if Linda borrowed a sum of $3350 at 6% simple interest for 3 years.

(4) What amount will be due after 2 years if Paul borrowed a sum of $3850 at a 6% simple interest?

(5) Calculate the amount due if Barbara borrowed a sum of $3550 at 8% simple interest for 3 years.

(6) Calculate the amount due after 10 years if Sarah borrowed a sum of $5850 at a rate of 7% simple interest.

(7) What amount does Robert have to pay after 5 years if he takes a loan of $3100 at 4% simple interest?

(8) Charles took a loan of $5800 at the rate of 7% simple interest per annum. If he paid an amount of $8236 to clear the loan, then find the time period of the loan.

(9) How much loan did Charles borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6785 to clear it?

(10) If Lisa paid $4374 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.