Simple Interest
Math MCQs

Question :    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) Matthew took a loan of $6400 at the rate of 7% simple interest per annum. If he paid an amount of $10432 to clear the loan, then find the time period of the loan.

(2) Nancy took a loan of $6300 at the rate of 9% simple interest per annum. If he paid an amount of $11970 to clear the loan, then find the time period of the loan.

(3) Calculate the amount due after 9 years if David borrowed a sum of $5400 at a rate of 8% simple interest.

(4) Karen had to pay $4424 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(5) What amount does James have to pay after 5 years if he takes a loan of $3000 at 7% simple interest?

(6) What amount does Thomas have to pay after 6 years if he takes a loan of $3800 at 7% simple interest?

(7) Calculate the amount due after 10 years if Sarah borrowed a sum of $5850 at a rate of 4% simple interest.

(8) Calculate the amount due after 9 years if Joseph borrowed a sum of $5700 at a rate of 2% simple interest.

(9) Joseph took a loan of $5400 at the rate of 6% simple interest per annum. If he paid an amount of $8316 to clear the loan, then find the time period of the loan.

(10) What amount does Karen have to pay after 6 years if he takes a loan of $3950 at 7% simple interest?