Simple Interest
Math MCQs

Question :    If Jessica paid $4500 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

Correct Answer  $3750

Solution & Explanation

Solution

Given,

Amount (A) = $4500

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

$4500 = P (1 + 5% × 4)

⇒ $4500 = P (1 + ⁵/₁₀₀ × 4)

⇒ $4500 = P (1 + ^{5 × 4}/₁₀₀)

⇒ $4500 = P (1 + ²⁰/₁₀₀)

⇒ $4500 = P (^{100 + 20}/₁₀₀)

⇒ $4500 = P × ¹²⁰/₁₀₀

⇒ P × ¹²⁰/₁₀₀ = $4500

⇒ P = ⁴⁵⁰⁰/_¹²⁰/100

⇒ P = 4500 × ¹⁰⁰/₁₂₀

⇒ P = ^{4500 × 100}/₁₂₀

⇒ P = ⁴⁵⁰⁰⁰⁰/₁₂₀

⇒ P = $3750

Thus, the sum borrowed (P) = $3750 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 4500, then the Principal = ¹⁰⁰/₁₂₀ × 4500

= ^{100 × 4500}/₁₂₀

= ⁴⁵⁰⁰⁰⁰/₁₂₀

= 3750

Thus, Principal = $3750

Thus, the sum borrowed = $3750 Answer

Similar Questions

(1) If Emily paid $5320 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(2) What amount does Patricia have to pay after 5 years if he takes a loan of $3150 at 4% simple interest?

(3) Robert took a loan of $4200 at the rate of 6% simple interest per annum. If he paid an amount of $6720 to clear the loan, then find the time period of the loan.

(4) Linda had to pay $3852.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(5) What amount does Christopher have to pay after 5 years if he takes a loan of $4000 at 9% simple interest?

(6) Richard took a loan of $5200 at the rate of 6% simple interest per annum. If he paid an amount of $7696 to clear the loan, then find the time period of the loan.

(7) Find the amount to be paid if David borrowed a sum of $5400 at 7% simple interest for 7 years.

(8) Nancy took a loan of $6300 at the rate of 8% simple interest per annum. If he paid an amount of $11340 to clear the loan, then find the time period of the loan.

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

(10) What amount will be due after 2 years if William borrowed a sum of $3250 at a 7% simple interest?