Simple Interest
Math MCQs

Question :    If Anthony paid $5160 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

Correct Answer  $4300

Solution & Explanation

Solution

Given,

Amount (A) = $5160

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

$5160 = P (1 + 5% × 4)

⇒ $5160 = P (1 + ⁵/₁₀₀ × 4)

⇒ $5160 = P (1 + ^{5 × 4}/₁₀₀)

⇒ $5160 = P (1 + ²⁰/₁₀₀)

⇒ $5160 = P (^{100 + 20}/₁₀₀)

⇒ $5160 = P × ¹²⁰/₁₀₀

⇒ P × ¹²⁰/₁₀₀ = $5160

⇒ P = ⁵¹⁶⁰/_¹²⁰/100

⇒ P = 5160 × ¹⁰⁰/₁₂₀

⇒ P = ^{5160 × 100}/₁₂₀

⇒ P = ⁵¹⁶⁰⁰⁰/₁₂₀

⇒ P = $4300

Thus, the sum borrowed (P) = $4300 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 5160, then the Principal = ¹⁰⁰/₁₂₀ × 5160

= ^{100 × 5160}/₁₂₀

= ⁵¹⁶⁰⁰⁰/₁₂₀

= 4300

Thus, Principal = $4300

Thus, the sum borrowed = $4300 Answer

Similar Questions

(1) Barbara had to pay $3976 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(2) What amount will be due after 2 years if Donald borrowed a sum of $3750 at a 7% simple interest?

(3) David took a loan of $4800 at the rate of 8% simple interest per annum. If he paid an amount of $8256 to clear the loan, then find the time period of the loan.

(4) Calculate the amount due after 9 years if John borrowed a sum of $5200 at a rate of 4% simple interest.

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

(6) 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.

(7) Lisa took a loan of $6100 at the rate of 9% simple interest per annum. If he paid an amount of $9394 to clear the loan, then find the time period of the loan.

(8) If Betty paid $5100 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(9) James took a loan of $4000 at the rate of 8% simple interest per annum. If he paid an amount of $6240 to clear the loan, then find the time period of the loan.

(10) Calculate the amount due if William borrowed a sum of $3500 at 8% simple interest for 3 years.