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) Find the amount to be paid if John borrowed a sum of $5200 at 7% simple interest for 8 years.

(2) Calculate the amount due if Richard borrowed a sum of $3600 at 9% simple interest for 3 years.

(3) In how much time a principal of $3050 will amount to $3172 at a simple interest of 2% per annum?

(4) In how much time a principal of $3050 will amount to $3324.5 at a simple interest of 3% per annum?

(5) How much loan did Robert borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $5865 to clear it?

(6) Richard had to pay $4032 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(7) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 3% simple interest?

(8) How much loan did Joshua borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8625 to clear it?

(9) Anthony took a loan of $6600 at the rate of 7% simple interest per annum. If he paid an amount of $11220 to clear the loan, then find the time period of the loan.

(10) Find the amount to be paid if Susan borrowed a sum of $5650 at 4% simple interest for 8 years.