Simple Interest
Math MCQs

Question :    If Barbara paid $4260 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

Correct Answer  $3550

Solution & Explanation

Solution

Given,

Amount (A) = $4260

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

$4260 = P (1 + 5% × 4)

⇒ $4260 = P (1 + ⁵/₁₀₀ × 4)

⇒ $4260 = P (1 + ^{5 × 4}/₁₀₀)

⇒ $4260 = P (1 + ²⁰/₁₀₀)

⇒ $4260 = P (^{100 + 20}/₁₀₀)

⇒ $4260 = P × ¹²⁰/₁₀₀

⇒ P × ¹²⁰/₁₀₀ = $4260

⇒ P = ⁴²⁶⁰/_¹²⁰/100

⇒ P = 4260 × ¹⁰⁰/₁₂₀

⇒ P = ^{4260 × 100}/₁₂₀

⇒ P = ⁴²⁶⁰⁰⁰/₁₂₀

⇒ P = $3550

Thus, the sum borrowed (P) = $3550 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 4260, then the Principal = ¹⁰⁰/₁₂₀ × 4260

= ^{100 × 4260}/₁₂₀

= ⁴²⁶⁰⁰⁰/₁₂₀

= 3550

Thus, Principal = $3550

Thus, the sum borrowed = $3550 Answer

Similar Questions

(1) Find the amount to be paid if Patricia borrowed a sum of $5150 at 4% simple interest for 8 years.

(2) Find the amount to be paid if Richard borrowed a sum of $5600 at 6% simple interest for 8 years.

(3) What amount does Robert have to pay after 6 years if he takes a loan of $3100 at 9% simple interest?

(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) Steven had to pay $4876 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(6) William took a loan of $5000 at the rate of 6% simple interest per annum. If he paid an amount of $7400 to clear the loan, then find the time period of the loan.

(7) Barbara took a loan of $5100 at the rate of 10% simple interest per annum. If he paid an amount of $8160 to clear the loan, then find the time period of the loan.

(8) What amount will be due after 2 years if Charles borrowed a sum of $3450 at a 9% simple interest?

(9) Karen took a loan of $5900 at the rate of 8% simple interest per annum. If he paid an amount of $9204 to clear the loan, then find the time period of the loan.

(10) Calculate the amount due after 10 years if Jessica borrowed a sum of $5750 at a rate of 2% simple interest.