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) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 7% simple interest for 7 years.

(2) How much loan did Daniel borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7625 to clear it?

(3) What amount does Thomas have to pay after 5 years if he takes a loan of $3800 at 6% simple interest?

(4) Calculate the amount due after 9 years if Linda borrowed a sum of $5350 at a rate of 8% simple interest.

(5) Find the amount to be paid if David borrowed a sum of $5400 at 8% simple interest for 7 years.

(6) What amount does Jennifer have to pay after 5 years if he takes a loan of $3250 at 7% simple interest?

(7) Calculate the amount due if Linda borrowed a sum of $3350 at 5% simple interest for 3 years.

(8) Calculate the amount due after 10 years if Charles borrowed a sum of $5900 at a rate of 8% simple interest.

(9) Daniel took a loan of $6200 at the rate of 6% simple interest per annum. If he paid an amount of $9176 to clear the loan, then find the time period of the loan.

(10) Sandra took a loan of $6900 at the rate of 7% simple interest per annum. If he paid an amount of $10764 to clear the loan, then find the time period of the loan.