Simple Interest
Math MCQs

Question :    If Steven paid $5520 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

Correct Answer  $4600

Solution & Explanation

Solution

Given,

Amount (A) = $5520

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

$5520 = P (1 + 5% × 4)

⇒ $5520 = P (1 + ⁵/₁₀₀ × 4)

⇒ $5520 = P (1 + ^{5 × 4}/₁₀₀)

⇒ $5520 = P (1 + ²⁰/₁₀₀)

⇒ $5520 = P (^{100 + 20}/₁₀₀)

⇒ $5520 = P × ¹²⁰/₁₀₀

⇒ P × ¹²⁰/₁₀₀ = $5520

⇒ P = ⁵⁵²⁰/_¹²⁰/100

⇒ P = 5520 × ¹⁰⁰/₁₂₀

⇒ P = ^{5520 × 100}/₁₂₀

⇒ P = ⁵⁵²⁰⁰⁰/₁₂₀

⇒ P = $4600

Thus, the sum borrowed (P) = $4600 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 5520, then the Principal = ¹⁰⁰/₁₂₀ × 5520

= ^{100 × 5520}/₁₂₀

= ⁵⁵²⁰⁰⁰/₁₂₀

= 4600

Thus, Principal = $4600

Thus, the sum borrowed = $4600 Answer

Similar Questions

(1) What amount will be due after 2 years if Andrew borrowed a sum of $3900 at a 4% simple interest?

(2) What amount does William have to pay after 5 years if he takes a loan of $3500 at 10% simple interest?

(3) Calculate the amount due after 10 years if Linda borrowed a sum of $5350 at a rate of 6% simple interest.

(4) John took a loan of $4400 at the rate of 10% simple interest per annum. If he paid an amount of $7480 to clear the loan, then find the time period of the loan.

(5) Calculate the amount due after 10 years if Mary borrowed a sum of $5050 at a rate of 2% simple interest.

(6) If Steven paid $4968 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(7) Find the amount to be paid if Linda borrowed a sum of $5350 at 3% simple interest for 7 years.

(8) In how much time a principal of $3050 will amount to $3294 at a simple interest of 2% per annum?

(9) Calculate the amount due if Jennifer borrowed a sum of $3250 at 9% simple interest for 3 years.

(10) Find the amount to be paid if James borrowed a sum of $5000 at 5% simple interest for 8 years.