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 if John borrowed a sum of $3200 at 2% simple interest for 3 years.

(2) Robert took a loan of $4200 at the rate of 8% simple interest per annum. If he paid an amount of $7560 to clear the loan, then find the time period of the loan.

(3) Calculate the amount due if Jessica borrowed a sum of $3750 at 9% simple interest for 4 years.

(4) William took a loan of $5000 at the rate of 7% simple interest per annum. If he paid an amount of $8500 to clear the loan, then find the time period of the loan.

(5) Betty took a loan of $6500 at the rate of 7% simple interest per annum. If he paid an amount of $9230 to clear the loan, then find the time period of the loan.

(6) If Thomas paid $4256 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(7) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 9% simple interest?

(8) Lisa took a loan of $6100 at the rate of 7% simple interest per annum. If he paid an amount of $10370 to clear the loan, then find the time period of the loan.

(9) What amount does Christopher have to pay after 6 years if he takes a loan of $4000 at 3% simple interest?

(10) What amount does Patricia have to pay after 6 years if he takes a loan of $3150 at 7% simple interest?