Simple Interest
Math MCQs

Question :    How much loan did Jacob borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $9200 to clear it?

Correct Answer  $8000

Solution & Explanation

Solution

Given,

Amount (A) = $9200

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

$9200 = P (1 + 3% × 5)

⇒ $9200 = P (1 + ³/₁₀₀ × 5)

⇒ $9200 = P (1 + ^{3 × 5}/₁₀₀)

⇒ $9200 = P (1 + ¹⁵/₁₀₀)

⇒ $9200 = P (^{100 + 15}/₁₀₀)

⇒ $9200 = P × ¹¹⁵/₁₀₀

⇒ P × ¹¹⁵/₁₀₀ = $9200

⇒ P = ⁹²⁰⁰/_¹¹⁵/100

⇒ P = 9200 × ¹⁰⁰/₁₁₅

⇒ P = ^{9200 × 100}/₁₁₅

⇒ P = ⁹²⁰⁰⁰⁰/₁₁₅

⇒ P = $8000

Thus, the sum borrowed (P) = $8000 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 9200, then the Principal = ¹⁰⁰/₁₁₅ × 9200

= ^{100 × 9200}/₁₁₅

= ⁹²⁰⁰⁰⁰/₁₁₅

= 8000

Thus, Principal = $8000

Thus, the sum borrowed = $8000 Answer

Similar Questions

(1) What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 6% simple interest?

(2) Matthew took a loan of $6400 at the rate of 10% simple interest per annum. If he paid an amount of $11520 to clear the loan, then find the time period of the loan.

(3) Calculate the amount due if Thomas borrowed a sum of $3800 at 5% simple interest for 4 years.

(4) Patricia took a loan of $4300 at the rate of 7% simple interest per annum. If he paid an amount of $6106 to clear the loan, then find the time period of the loan.

(5) If Betty paid $4760 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(6) Sandra took a loan of $6900 at the rate of 7% simple interest per annum. If he paid an amount of $9798 to clear the loan, then find the time period of the loan.

(7) What amount does Patricia have to pay after 5 years if he takes a loan of $3150 at 6% simple interest?

(8) Sarah took a loan of $5700 at the rate of 6% simple interest per annum. If he paid an amount of $8094 to clear the loan, then find the time period of the loan.

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

(10) How much loan did Susan borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6780 to clear it?