Simple Interest
Math MCQs

Question :  ( 1 of 10 )  How much loan did Ronald borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8625 to clear it?

Correct Answer  $7500

Solution & Explanation

Solution

Given,

Amount (A) = $8625

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

$8625 = P (1 + 3% × 5)

⇒ $8625 = P (1 + ³/₁₀₀ × 5)

⇒ $8625 = P (1 + ^{3 × 5}/₁₀₀)

⇒ $8625 = P (1 + ¹⁵/₁₀₀)

⇒ $8625 = P (^{100 + 15}/₁₀₀)

⇒ $8625 = P × ¹¹⁵/₁₀₀

⇒ P × ¹¹⁵/₁₀₀ = $8625

⇒ P = ⁸⁶²⁵/_¹¹⁵/100

⇒ P = 8625 × ¹⁰⁰/₁₁₅

⇒ P = ^{8625 × 100}/₁₁₅

⇒ P = ⁸⁶²⁵⁰⁰/₁₁₅

⇒ P = $7500

Thus, the sum borrowed (P) = $7500 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 8625, then the Principal = ¹⁰⁰/₁₁₅ × 8625

= ^{100 × 8625}/₁₁₅

= ⁸⁶²⁵⁰⁰/₁₁₅

= 7500

Thus, Principal = $7500

Thus, the sum borrowed = $7500 Answer

Similar Questions

(1) Calculate the amount due after 9 years if Mary borrowed a sum of $5050 at a rate of 4% simple interest.

(2) What amount will be due after 2 years if Andrew borrowed a sum of $3900 at a 10% simple interest?

(3) Calculate the amount due if Michael borrowed a sum of $3300 at 7% simple interest for 4 years.

(4) How much loan did Laura borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9812.5 to clear it?

(5) Find the amount to be paid if Linda borrowed a sum of $5350 at 8% simple interest for 7 years.

(6) Thomas took a loan of $5600 at the rate of 6% simple interest per annum. If he paid an amount of $8288 to clear the loan, then find the time period of the loan.

(7) Mary took a loan of $4100 at the rate of 8% simple interest per annum. If he paid an amount of $6396 to clear the loan, then find the time period of the loan.

(8) Anthony took a loan of $6600 at the rate of 9% simple interest per annum. If he paid an amount of $10164 to clear the loan, then find the time period of the loan.

(9) Linda had to pay $3752 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(10) How much loan did Laura borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9420 to clear it?