Simple Interest
Math MCQs

Question :    If Donna paid $5820 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

Correct Answer  $4850

Solution & Explanation

Solution

Given,

Amount (A) = $5820

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

$5820 = P (1 + 5% × 4)

⇒ $5820 = P (1 + ⁵/₁₀₀ × 4)

⇒ $5820 = P (1 + ^{5 × 4}/₁₀₀)

⇒ $5820 = P (1 + ²⁰/₁₀₀)

⇒ $5820 = P (^{100 + 20}/₁₀₀)

⇒ $5820 = P × ¹²⁰/₁₀₀

⇒ P × ¹²⁰/₁₀₀ = $5820

⇒ P = ⁵⁸²⁰/_¹²⁰/100

⇒ P = 5820 × ¹⁰⁰/₁₂₀

⇒ P = ^{5820 × 100}/₁₂₀

⇒ P = ⁵⁸²⁰⁰⁰/₁₂₀

⇒ P = $4850

Thus, the sum borrowed (P) = $4850 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 5820, then the Principal = ¹⁰⁰/₁₂₀ × 5820

= ^{100 × 5820}/₁₂₀

= ⁵⁸²⁰⁰⁰/₁₂₀

= 4850

Thus, Principal = $4850

Thus, the sum borrowed = $4850 Answer

Similar Questions

(1) John took a loan of $4400 at the rate of 10% simple interest per annum. If he paid an amount of $8360 to clear the loan, then find the time period of the loan.

(2) Susan took a loan of $5300 at the rate of 6% simple interest per annum. If he paid an amount of $8162 to clear the loan, then find the time period of the loan.

(3) Calculate the amount due after 9 years if Karen borrowed a sum of $5950 at a rate of 10% simple interest.

(4) Calculate the amount due if Thomas borrowed a sum of $3800 at 2% simple interest for 4 years.

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

(6) Find the amount to be paid if Christopher borrowed a sum of $6000 at 4% simple interest for 8 years.

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

(8) Calculate the amount due after 10 years if Charles borrowed a sum of $5900 at a rate of 5% simple interest.

(9) What amount does Patricia have to pay after 6 years if he takes a loan of $3150 at 9% simple interest?

(10) Jessica took a loan of $5500 at the rate of 10% simple interest per annum. If he paid an amount of $9350 to clear the loan, then find the time period of the loan.