Simple Interest
Math MCQs

Question :    If Susan paid $4380 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

Correct Answer  $3650

Solution & Explanation

Solution

Given,

Amount (A) = $4380

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

$4380 = P (1 + 5% × 4)

⇒ $4380 = P (1 + ⁵/₁₀₀ × 4)

⇒ $4380 = P (1 + ^{5 × 4}/₁₀₀)

⇒ $4380 = P (1 + ²⁰/₁₀₀)

⇒ $4380 = P (^{100 + 20}/₁₀₀)

⇒ $4380 = P × ¹²⁰/₁₀₀

⇒ P × ¹²⁰/₁₀₀ = $4380

⇒ P = ⁴³⁸⁰/_¹²⁰/100

⇒ P = 4380 × ¹⁰⁰/₁₂₀

⇒ P = ^{4380 × 100}/₁₂₀

⇒ P = ⁴³⁸⁰⁰⁰/₁₂₀

⇒ 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 = 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 4380, then the Principal = ¹⁰⁰/₁₂₀ × 4380

= ^{100 × 4380}/₁₂₀

= ⁴³⁸⁰⁰⁰/₁₂₀

= 3650

Thus, Principal = $3650

Thus, the sum borrowed = $3650 Answer

Similar Questions

(1) Mary took a loan of $4100 at the rate of 9% simple interest per annum. If he paid an amount of $7052 to clear the loan, then find the time period of the loan.

(2) How much loan did Steven borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7920 to clear it?

(3) Betty took a loan of $6500 at the rate of 9% simple interest per annum. If he paid an amount of $11180 to clear the loan, then find the time period of the loan.

(4) What amount will be due after 2 years if Mark borrowed a sum of $3700 at a 7% simple interest?

(5) Find the amount to be paid if Jessica borrowed a sum of $5750 at 5% simple interest for 7 years.

(6) Find the amount to be paid if Richard borrowed a sum of $5600 at 9% simple interest for 7 years.

(7) Calculate the amount due if Robert borrowed a sum of $3100 at 8% simple interest for 4 years.

(8) Calculate the amount due if Christopher borrowed a sum of $4000 at 2% simple interest for 3 years.

(9) What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 3% simple interest?

(10) Calculate the amount due if Sarah borrowed a sum of $3850 at 2% simple interest for 3 years.