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) Calculate the amount due after 10 years if Karen borrowed a sum of $5950 at a rate of 7% simple interest.

(2) Margaret took a loan of $6700 at the rate of 8% simple interest per annum. If he paid an amount of $10452 to clear the loan, then find the time period of the loan.

(3) What amount will be due after 2 years if Joseph borrowed a sum of $3350 at a 7% simple interest?

(4) What amount does John have to pay after 6 years if he takes a loan of $3200 at 6% simple interest?

(5) Calculate the amount due if Charles borrowed a sum of $3900 at 10% simple interest for 3 years.

(6) Barbara took a loan of $5100 at the rate of 6% simple interest per annum. If he paid an amount of $6936 to clear the loan, then find the time period of the loan.

(7) What amount will be due after 2 years if Richard borrowed a sum of $3300 at a 4% simple interest?

(8) Calculate the amount due if James borrowed a sum of $3000 at 7% simple interest for 3 years.

(9) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 8% simple interest for 8 years.

(10) Find the amount to be paid if Robert borrowed a sum of $5100 at 6% simple interest for 7 years.