Simple Interest
Math MCQs

Question :    How much loan did Cynthia borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9540 to clear it?

Correct Answer  $7950

Solution & Explanation

Solution

Given,

Amount (A) = $9540

Rate of Simple Interest (R) = 4%

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

$9540 = P (1 + 4% × 5)

⇒ $9540 = P (1 + ⁴/₁₀₀ × 5)

⇒ $9540 = P (1 + ^{4 × 5}/₁₀₀)

⇒ $9540 = P (1 + ²⁰/₁₀₀)

⇒ $9540 = P (^{100 + 20}/₁₀₀)

⇒ $9540 = P × ¹²⁰/₁₀₀

⇒ P × ¹²⁰/₁₀₀ = $9540

⇒ P = ⁹⁵⁴⁰/_¹²⁰/100

⇒ P = 9540 × ¹⁰⁰/₁₂₀

⇒ P = ^{9540 × 100}/₁₂₀

⇒ P = ⁹⁵⁴⁰⁰⁰/₁₂₀

⇒ 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 = 4% per annum

Thus, Interest = 4% of principal

⇒ Interest = 4% of 100 = 4

Thus, Simple Interest for 1 year = 4

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 × 4 = 20

Thus, simple interest for 5 years = 20

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 20 = 120

Calculation of the Principal

Now,

∵ If the Amount is 120, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₂₀

∴ If the Amount is 9540, then the Principal = ¹⁰⁰/₁₂₀ × 9540

= ^{100 × 9540}/₁₂₀

= ⁹⁵⁴⁰⁰⁰/₁₂₀

= 7950

Thus, Principal = $7950

Thus, the sum borrowed = $7950 Answer

Similar Questions

(1) In how much time a principal of $3150 will amount to $3622.5 at a simple interest of 5% per annum?

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

(3) Jessica took a loan of $5500 at the rate of 6% simple interest per annum. If he paid an amount of $8800 to clear the loan, then find the time period of the loan.

(4) David had to pay $3706 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(5) Daniel had to pay $4346 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(6) Karen had to pay $4305.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(7) Calculate the amount due if Sarah borrowed a sum of $3850 at 5% simple interest for 4 years.

(8) If Linda paid $3752 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(9) Emily had to pay $5462.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(10) Find the amount to be paid if Karen borrowed a sum of $5950 at 7% simple interest for 8 years.