Simple Interest
Math MCQs

Question :    If Mary paid $3538 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

Correct Answer  $3050

Solution & Explanation

Solution

Given,

Amount (A) = $3538

Rate of Simple Interest (R) = 4%

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

$3538 = P (1 + 4% × 4)

⇒ $3538 = P (1 + ⁴/₁₀₀ × 4)

⇒ $3538 = P (1 + ^{4 × 4}/₁₀₀)

⇒ $3538 = P (1 + ¹⁶/₁₀₀)

⇒ $3538 = P (^{100 + 16}/₁₀₀)

⇒ $3538 = P × ¹¹⁶/₁₀₀

⇒ P × ¹¹⁶/₁₀₀ = $3538

⇒ P = ³⁵³⁸/_¹¹⁶/100

⇒ P = 3538 × ¹⁰⁰/₁₁₆

⇒ P = ^{3538 × 100}/₁₁₆

⇒ P = ³⁵³⁸⁰⁰/₁₁₆

⇒ P = $3050

Thus, the sum borrowed (P) = $3050 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 = 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 × 4 = 16

Thus, simple interest for 4 years = 16

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 16 = 116

Calculation of the Principal

Now,

∵ If the Amount is 116, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₁₆

∴ If the Amount is 3538, then the Principal = ¹⁰⁰/₁₁₆ × 3538

= ^{100 × 3538}/₁₁₆

= ³⁵³⁸⁰⁰/₁₁₆

= 3050

Thus, Principal = $3050

Thus, the sum borrowed = $3050 Answer

Similar Questions

(1) Thomas took a loan of $5600 at the rate of 7% simple interest per annum. If he paid an amount of $9128 to clear the loan, then find the time period of the loan.

(2) What amount does Robert have to pay after 6 years if he takes a loan of $3100 at 9% simple interest?

(3) Barbara took a loan of $5100 at the rate of 7% simple interest per annum. If he paid an amount of $7956 to clear the loan, then find the time period of the loan.

(4) How much loan did Amanda borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7865 to clear it?

(5) Calculate the amount due after 9 years if Sarah borrowed a sum of $5850 at a rate of 5% simple interest.

(6) What amount does Mary have to pay after 6 years if he takes a loan of $3050 at 4% simple interest?

(7) If Lisa paid $4698 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(8) Calculate the amount due if Linda borrowed a sum of $3350 at 5% simple interest for 4 years.

(9) 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?

(10) Find the amount to be paid if Christopher borrowed a sum of $6000 at 6% simple interest for 7 years.