Simple Interest
Math MCQs

Question :    If Patricia paid $3780 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

Correct Answer  $3150

Solution & Explanation

Solution

Given,

Amount (A) = $3780

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

$3780 = P (1 + 5% × 4)

⇒ $3780 = P (1 + ⁵/₁₀₀ × 4)

⇒ $3780 = P (1 + ^{5 × 4}/₁₀₀)

⇒ $3780 = P (1 + ²⁰/₁₀₀)

⇒ $3780 = P (^{100 + 20}/₁₀₀)

⇒ $3780 = P × ¹²⁰/₁₀₀

⇒ P × ¹²⁰/₁₀₀ = $3780

⇒ P = ³⁷⁸⁰/_¹²⁰/100

⇒ P = 3780 × ¹⁰⁰/₁₂₀

⇒ P = ^{3780 × 100}/₁₂₀

⇒ P = ³⁷⁸⁰⁰⁰/₁₂₀

⇒ P = $3150

Thus, the sum borrowed (P) = $3150 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 3780, then the Principal = ¹⁰⁰/₁₂₀ × 3780

= ^{100 × 3780}/₁₂₀

= ³⁷⁸⁰⁰⁰/₁₂₀

= 3150

Thus, Principal = $3150

Thus, the sum borrowed = $3150 Answer

Similar Questions

(1) How much loan did George borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8760 to clear it?

(2) How much loan did Margaret borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7302.5 to clear it?

(3) Daniel had to pay $4715 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(4) What amount does Joseph have to pay after 6 years if he takes a loan of $3700 at 9% simple interest?

(5) What amount does Christopher have to pay after 6 years if he takes a loan of $4000 at 10% simple interest?

(6) Calculate the amount due if Christopher borrowed a sum of $4000 at 5% simple interest for 3 years.

(7) Find the amount to be paid if John borrowed a sum of $5200 at 4% simple interest for 7 years.

(8) Calculate the amount due if Jessica borrowed a sum of $3750 at 4% simple interest for 4 years.

(9) What amount does Jennifer have to pay after 5 years if he takes a loan of $3250 at 2% simple interest?

(10) Calculate the amount due if Michael borrowed a sum of $3300 at 4% simple interest for 4 years.