Simple Interest
Math MCQs

Question :    How much loan did Cynthia borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $9142.5 to clear it?

Correct Answer  $7950

Solution & Explanation

Solution

Given,

Amount (A) = $9142.5

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

$9142.5 = P (1 + 3% × 5)

⇒ $9142.5 = P (1 + ³/₁₀₀ × 5)

⇒ $9142.5 = P (1 + ^{3 × 5}/₁₀₀)

⇒ $9142.5 = P (1 + ¹⁵/₁₀₀)

⇒ $9142.5 = P (^{100 + 15}/₁₀₀)

⇒ $9142.5 = P × ¹¹⁵/₁₀₀

⇒ P × ¹¹⁵/₁₀₀ = $9142.5

⇒ P = ^9142.5/_¹¹⁵/100

⇒ P = 9142.5 × ¹⁰⁰/₁₁₅

⇒ P = ^{9142.5 × 100}/₁₁₅

⇒ P = ⁹¹⁴²⁵⁰/₁₁₅

⇒ P = $7950

Thus, the sum borrowed (P) = $7950 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 9142.5, then the Principal = ¹⁰⁰/₁₁₅ × 9142.5

= ^{100 × 9142.5}/₁₁₅

= ⁹¹⁴²⁵⁰/₁₁₅

= 7950

Thus, Principal = $7950

Thus, the sum borrowed = $7950 Answer

Similar Questions

(1) Jennifer took a loan of $4500 at the rate of 9% simple interest per annum. If he paid an amount of $7740 to clear the loan, then find the time period of the loan.

(2) Calculate the amount due after 9 years if Charles borrowed a sum of $5900 at a rate of 7% simple interest.

(3) In how much time a principal of $3050 will amount to $3233 at a simple interest of 3% per annum?

(4) How much loan did Kimberly borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7315 to clear it?

(5) What amount will be due after 2 years if John borrowed a sum of $3100 at a 10% simple interest?

(6) Calculate the amount due after 9 years if Christopher borrowed a sum of $6000 at a rate of 10% simple interest.

(7) Susan took a loan of $5300 at the rate of 7% simple interest per annum. If he paid an amount of $9010 to clear the loan, then find the time period of the loan.

(8) Calculate the amount due after 9 years if Jessica borrowed a sum of $5750 at a rate of 10% simple interest.

(9) If Mark paid $5280 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(10) Matthew had to pay $4830 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.