Simple Interest
Math MCQs

Question :    If Susan paid $4088 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

Correct Answer  $3650

Solution & Explanation

Solution

Given,

Amount (A) = $4088

Rate of Simple Interest (R) = 3%

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

$4088 = P (1 + 3% × 4)

⇒ $4088 = P (1 + ³/₁₀₀ × 4)

⇒ $4088 = P (1 + ^{3 × 4}/₁₀₀)

⇒ $4088 = P (1 + ¹²/₁₀₀)

⇒ $4088 = P (^{100 + 12}/₁₀₀)

⇒ $4088 = P × ¹¹²/₁₀₀

⇒ P × ¹¹²/₁₀₀ = $4088

⇒ P = ⁴⁰⁸⁸/_¹¹²/100

⇒ P = 4088 × ¹⁰⁰/₁₁₂

⇒ P = ^{4088 × 100}/₁₁₂

⇒ P = ⁴⁰⁸⁸⁰⁰/₁₁₂

⇒ P = $3650

Thus, the sum borrowed (P) = $3650 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 = 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 × 3 = 12

Thus, simple interest for 4 years = 12

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 12 = 112

Calculation of the Principal

Now,

∵ If the Amount is 112, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₁₂

∴ If the Amount is 4088, then the Principal = ¹⁰⁰/₁₁₂ × 4088

= ^{100 × 4088}/₁₁₂

= ⁴⁰⁸⁸⁰⁰/₁₁₂

= 3650

Thus, Principal = $3650

Thus, the sum borrowed = $3650 Answer

Similar Questions

(1) Charles took a loan of $5800 at the rate of 10% simple interest per annum. If he paid an amount of $10440 to clear the loan, then find the time period of the loan.

(2) What amount does Joseph have to pay after 6 years if he takes a loan of $3700 at 3% simple interest?

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

(4) Linda took a loan of $4700 at the rate of 7% simple interest per annum. If he paid an amount of $7661 to clear the loan, then find the time period of the loan.

(5) Calculate the amount due if David borrowed a sum of $3400 at 9% simple interest for 3 years.

(6) How much loan did Michelle borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8340 to clear it?

(7) If Matthew paid $5040 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(8) How much loan did David borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5940 to clear it?

(9) What amount does Charles have to pay after 6 years if he takes a loan of $3900 at 5% simple interest?

(10) Christopher took a loan of $6000 at the rate of 10% simple interest per annum. If he paid an amount of $10800 to clear the loan, then find the time period of the loan.