Simple Interest
Math MCQs

Question :    If Emily paid $5700 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

Correct Answer  $4750

Solution & Explanation

Solution

Given,

Amount (A) = $5700

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

$5700 = P (1 + 5% × 4)

⇒ $5700 = P (1 + ⁵/₁₀₀ × 4)

⇒ $5700 = P (1 + ^{5 × 4}/₁₀₀)

⇒ $5700 = P (1 + ²⁰/₁₀₀)

⇒ $5700 = P (^{100 + 20}/₁₀₀)

⇒ $5700 = P × ¹²⁰/₁₀₀

⇒ P × ¹²⁰/₁₀₀ = $5700

⇒ P = ⁵⁷⁰⁰/_¹²⁰/100

⇒ P = 5700 × ¹⁰⁰/₁₂₀

⇒ P = ^{5700 × 100}/₁₂₀

⇒ P = ⁵⁷⁰⁰⁰⁰/₁₂₀

⇒ P = $4750

Thus, the sum borrowed (P) = $4750 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 5700, then the Principal = ¹⁰⁰/₁₂₀ × 5700

= ^{100 × 5700}/₁₂₀

= ⁵⁷⁰⁰⁰⁰/₁₂₀

= 4750

Thus, Principal = $4750

Thus, the sum borrowed = $4750 Answer

Similar Questions

(1) Michael took a loan of $4600 at the rate of 6% simple interest per annum. If he paid an amount of $7084 to clear the loan, then find the time period of the loan.

(2) Calculate the amount due if Michael borrowed a sum of $3300 at 8% simple interest for 3 years.

(3) Calculate the amount due after 9 years if James borrowed a sum of $5000 at a rate of 6% simple interest.

(4) Calculate the amount due if William borrowed a sum of $3500 at 5% simple interest for 3 years.

(5) Kimberly had to pay $5347.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(6) Lisa took a loan of $6100 at the rate of 8% simple interest per annum. If he paid an amount of $9516 to clear the loan, then find the time period of the loan.

(7) Find the amount to be paid if David borrowed a sum of $5400 at 4% simple interest for 7 years.

(8) Calculate the amount due if Christopher borrowed a sum of $4000 at 6% simple interest for 3 years.

(9) Find the amount to be paid if Linda borrowed a sum of $5350 at 7% simple interest for 7 years.

(10) In how much time a principal of $3100 will amount to $3410 at a simple interest of 5% per annum?