Simple Interest
Math MCQs

Question :    If Steven paid $5520 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

Correct Answer  $4600

Solution & Explanation

Solution

Given,

Amount (A) = $5520

Rate of Simple Interest (R) = 5%

Time (T) = 4 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

$5520 = P (1 + 5% × 4)

⇒ $5520 = P (1 + ⁵/₁₀₀ × 4)

⇒ $5520 = P (1 + ^{5 × 4}/₁₀₀)

⇒ $5520 = P (1 + ²⁰/₁₀₀)

⇒ $5520 = P (^{100 + 20}/₁₀₀)

⇒ $5520 = P × ¹²⁰/₁₀₀

⇒ P × ¹²⁰/₁₀₀ = $5520

⇒ P = ⁵⁵²⁰/_¹²⁰/100

⇒ P = 5520 × ¹⁰⁰/₁₂₀

⇒ P = ^{5520 × 100}/₁₂₀

⇒ P = ⁵⁵²⁰⁰⁰/₁₂₀

⇒ P = $4600

Thus, the sum borrowed (P) = $4600 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 = 5% per annum

Thus, Interest = 5% of principal

⇒ Interest = 5% of 100 = 5

Thus, Simple Interest for 1 year = 5

Calculation of the Amount

Since, in the question, time = 4 years

So, we need to calculate the simple interest for the given time period, which is 4 years

Thus, Simple Interest for 4 years = 4 × Simple Interest for 1 year

= 4 × 5 = 20

Thus, simple interest for 4 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 5520, then the Principal = ¹⁰⁰/₁₂₀ × 5520

= ^{100 × 5520}/₁₂₀

= ⁵⁵²⁰⁰⁰/₁₂₀

= 4600

Thus, Principal = $4600

Thus, the sum borrowed = $4600 Answer

Similar Questions

(1) How much loan did Andrew borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7820 to clear it?

(2) Calculate the amount due after 9 years if Jennifer borrowed a sum of $5250 at a rate of 2% simple interest.

(3) Margaret had to pay $4611 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(4) Calculate the amount due if Robert borrowed a sum of $3100 at 6% simple interest for 3 years.

(5) In how much time a principal of $3050 will amount to $3538 at a simple interest of 4% per annum?

(6) Find the amount to be paid if Thomas borrowed a sum of $5800 at 7% simple interest for 7 years.

(7) Find the amount to be paid if Sarah borrowed a sum of $5850 at 4% simple interest for 7 years.

(8) If Steven paid $4968 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(9) If Margaret paid $4872 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(10) If Donna paid $5626 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.