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) Calculate the amount due after 10 years if Richard borrowed a sum of $5600 at a rate of 2% simple interest.

(2) Donald took a loan of $7000 at the rate of 6% simple interest per annum. If he paid an amount of $10780 to clear the loan, then find the time period of the loan.

(3) Calculate the amount due if James borrowed a sum of $3000 at 7% simple interest for 3 years.

(4) Calculate the amount due after 10 years if David borrowed a sum of $5400 at a rate of 9% simple interest.

(5) Mark took a loan of $6800 at the rate of 7% simple interest per annum. If he paid an amount of $11560 to clear the loan, then find the time period of the loan.

(6) Calculate the amount due after 10 years if Jessica borrowed a sum of $5750 at a rate of 8% simple interest.

(7) What amount does Jennifer have to pay after 6 years if he takes a loan of $3250 at 7% simple interest?

(8) Charles took a loan of $5800 at the rate of 6% simple interest per annum. If he paid an amount of $8584 to clear the loan, then find the time period of the loan.

(9) Patricia took a loan of $4300 at the rate of 6% simple interest per annum. If he paid an amount of $6880 to clear the loan, then find the time period of the loan.

(10) Calculate the amount due after 10 years if Susan borrowed a sum of $5650 at a rate of 4% simple interest.