Simple Interest
Math MCQs

Question :    How much loan did Donald borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7475 to clear it?

Correct Answer  $6500

Solution & Explanation

Solution

Given,

Amount (A) = $7475

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

$7475 = P (1 + 3% × 5)

⇒ $7475 = P (1 + ³/₁₀₀ × 5)

⇒ $7475 = P (1 + ^{3 × 5}/₁₀₀)

⇒ $7475 = P (1 + ¹⁵/₁₀₀)

⇒ $7475 = P (^{100 + 15}/₁₀₀)

⇒ $7475 = P × ¹¹⁵/₁₀₀

⇒ P × ¹¹⁵/₁₀₀ = $7475

⇒ P = ⁷⁴⁷⁵/_¹¹⁵/100

⇒ P = 7475 × ¹⁰⁰/₁₁₅

⇒ P = ^{7475 × 100}/₁₁₅

⇒ P = ⁷⁴⁷⁵⁰⁰/₁₁₅

⇒ P = $6500

Thus, the sum borrowed (P) = $6500 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 7475, then the Principal = ¹⁰⁰/₁₁₅ × 7475

= ^{100 × 7475}/₁₁₅

= ⁷⁴⁷⁵⁰⁰/₁₁₅

= 6500

Thus, Principal = $6500

Thus, the sum borrowed = $6500 Answer

Similar Questions

(1) Sarah took a loan of $5700 at the rate of 8% simple interest per annum. If he paid an amount of $9348 to clear the loan, then find the time period of the loan.

(2) Find the amount to be paid if Joseph borrowed a sum of $5700 at 10% simple interest for 8 years.

(3) James took a loan of $4000 at the rate of 8% simple interest per annum. If he paid an amount of $6560 to clear the loan, then find the time period of the loan.

(4) How much loan did Rebecca borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9562.5 to clear it?

(5) Sarah had to pay $4081 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(6) Patricia took a loan of $4300 at the rate of 9% simple interest per annum. If he paid an amount of $7396 to clear the loan, then find the time period of the loan.

(7) David took a loan of $4800 at the rate of 10% simple interest per annum. If he paid an amount of $8160 to clear the loan, then find the time period of the loan.

(8) Calculate the amount due after 9 years if Michael borrowed a sum of $5300 at a rate of 3% simple interest.

(9) Calculate the amount due after 10 years if Patricia borrowed a sum of $5150 at a rate of 8% simple interest.

(10) How much loan did Carol borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8107.5 to clear it?