Simple Interest
Math MCQs

Question :    If Thomas paid $4560 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

Correct Answer  $3800

Solution & Explanation

Solution

Given,

Amount (A) = $4560

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

$4560 = P (1 + 5% × 4)

⇒ $4560 = P (1 + ⁵/₁₀₀ × 4)

⇒ $4560 = P (1 + ^{5 × 4}/₁₀₀)

⇒ $4560 = P (1 + ²⁰/₁₀₀)

⇒ $4560 = P (^{100 + 20}/₁₀₀)

⇒ $4560 = P × ¹²⁰/₁₀₀

⇒ P × ¹²⁰/₁₀₀ = $4560

⇒ P = ⁴⁵⁶⁰/_¹²⁰/100

⇒ P = 4560 × ¹⁰⁰/₁₂₀

⇒ P = ^{4560 × 100}/₁₂₀

⇒ P = ⁴⁵⁶⁰⁰⁰/₁₂₀

⇒ P = $3800

Thus, the sum borrowed (P) = $3800 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 4560, then the Principal = ¹⁰⁰/₁₂₀ × 4560

= ^{100 × 4560}/₁₂₀

= ⁴⁵⁶⁰⁰⁰/₁₂₀

= 3800

Thus, Principal = $3800

Thus, the sum borrowed = $3800 Answer

Similar Questions

(1) Calculate the amount due after 10 years if Jessica borrowed a sum of $5750 at a rate of 9% simple interest.

(2) What amount does Thomas have to pay after 6 years if he takes a loan of $3800 at 6% simple interest?

(3) William took a loan of $5000 at the rate of 8% simple interest per annum. If he paid an amount of $8600 to clear the loan, then find the time period of the loan.

(4) Calculate the amount due if David borrowed a sum of $3400 at 5% simple interest for 4 years.

(5) Find the amount to be paid if Karen borrowed a sum of $5950 at 3% simple interest for 8 years.

(6) What amount will be due after 2 years if Andrew borrowed a sum of $3900 at a 6% simple interest?

(7) Calculate the amount due if Karen borrowed a sum of $3950 at 4% simple interest for 3 years.

(8) Find the amount to be paid if Mary borrowed a sum of $5050 at 3% simple interest for 8 years.

(9) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 2% simple interest for 4 years.

(10) Margaret took a loan of $6700 at the rate of 10% simple interest per annum. If he paid an amount of $13400 to clear the loan, then find the time period of the loan.