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 if Elizabeth borrowed a sum of $3450 at 3% simple interest for 3 years.

(2) What amount does Richard have to pay after 6 years if he takes a loan of $3600 at 2% simple interest?

(3) In how much time a principal of $3200 will amount to $3520 at a simple interest of 5% per annum?

(4) What amount does Robert have to pay after 5 years if he takes a loan of $3100 at 10% simple interest?

(5) Matthew took a loan of $6400 at the rate of 10% simple interest per annum. If he paid an amount of $10240 to clear the loan, then find the time period of the loan.

(6) How much loan did Mark borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7360 to clear it?

(7) Calculate the amount due after 10 years if James borrowed a sum of $5000 at a rate of 4% simple interest.

(8) Barbara had to pay $3869.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(9) Matthew took a loan of $6400 at the rate of 7% simple interest per annum. If he paid an amount of $10880 to clear the loan, then find the time period of the loan.

(10) Daniel took a loan of $6200 at the rate of 9% simple interest per annum. If he paid an amount of $10664 to clear the loan, then find the time period of the loan.