Simple Interest
Math MCQs

Question :    If Sandra paid $5340 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

Correct Answer  $4450

Solution & Explanation

Solution

Given,

Amount (A) = $5340

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

$5340 = P (1 + 5% × 4)

⇒ $5340 = P (1 + ⁵/₁₀₀ × 4)

⇒ $5340 = P (1 + ^{5 × 4}/₁₀₀)

⇒ $5340 = P (1 + ²⁰/₁₀₀)

⇒ $5340 = P (^{100 + 20}/₁₀₀)

⇒ $5340 = P × ¹²⁰/₁₀₀

⇒ P × ¹²⁰/₁₀₀ = $5340

⇒ P = ⁵³⁴⁰/_¹²⁰/100

⇒ P = 5340 × ¹⁰⁰/₁₂₀

⇒ P = ^{5340 × 100}/₁₂₀

⇒ P = ⁵³⁴⁰⁰⁰/₁₂₀

⇒ P = $4450

Thus, the sum borrowed (P) = $4450 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 5340, then the Principal = ¹⁰⁰/₁₂₀ × 5340

= ^{100 × 5340}/₁₂₀

= ⁵³⁴⁰⁰⁰/₁₂₀

= 4450

Thus, Principal = $4450

Thus, the sum borrowed = $4450 Answer

Similar Questions

(1) Donald took a loan of $7000 at the rate of 8% simple interest per annum. If he paid an amount of $12040 to clear the loan, then find the time period of the loan.

(2) Find the amount to be paid if Jessica borrowed a sum of $5750 at 10% simple interest for 7 years.

(3) Calculate the amount due after 9 years if Sarah borrowed a sum of $5850 at a rate of 3% simple interest.

(4) If Betty paid $4760 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(5) Sarah took a loan of $5700 at the rate of 9% simple interest per annum. If he paid an amount of $10830 to clear the loan, then find the time period of the loan.

(6) Calculate the amount due after 10 years if Karen borrowed a sum of $5950 at a rate of 4% simple interest.

(7) What amount does Susan have to pay after 6 years if he takes a loan of $3650 at 8% simple interest?

(8) How much loan did Paul borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8040 to clear it?

(9) Matthew took a loan of $6400 at the rate of 6% simple interest per annum. If he paid an amount of $9088 to clear the loan, then find the time period of the loan.

(10) Calculate the amount due if Karen borrowed a sum of $3950 at 4% simple interest for 3 years.