Simple Interest
Math MCQs

Question :    If Joseph paid $4440 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

Correct Answer  $3700

Solution & Explanation

Solution

Given,

Amount (A) = $4440

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

$4440 = P (1 + 5% × 4)

⇒ $4440 = P (1 + ⁵/₁₀₀ × 4)

⇒ $4440 = P (1 + ^{5 × 4}/₁₀₀)

⇒ $4440 = P (1 + ²⁰/₁₀₀)

⇒ $4440 = P (^{100 + 20}/₁₀₀)

⇒ $4440 = P × ¹²⁰/₁₀₀

⇒ P × ¹²⁰/₁₀₀ = $4440

⇒ P = ⁴⁴⁴⁰/_¹²⁰/100

⇒ P = 4440 × ¹⁰⁰/₁₂₀

⇒ P = ^{4440 × 100}/₁₂₀

⇒ P = ⁴⁴⁴⁰⁰⁰/₁₂₀

⇒ P = $3700

Thus, the sum borrowed (P) = $3700 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 4440, then the Principal = ¹⁰⁰/₁₂₀ × 4440

= ^{100 × 4440}/₁₂₀

= ⁴⁴⁴⁰⁰⁰/₁₂₀

= 3700

Thus, Principal = $3700

Thus, the sum borrowed = $3700 Answer

Similar Questions

(1) How much loan did David borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6750 to clear it?

(2) Calculate the amount due after 9 years if David borrowed a sum of $5400 at a rate of 4% simple interest.

(3) Find the amount to be paid if Jessica borrowed a sum of $5750 at 9% simple interest for 8 years.

(4) Richard took a loan of $5200 at the rate of 10% simple interest per annum. If he paid an amount of $10400 to clear the loan, then find the time period of the loan.

(5) Calculate the amount due after 10 years if Richard borrowed a sum of $5600 at a rate of 6% simple interest.

(6) How much loan did Ronald borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8625 to clear it?

(7) Robert took a loan of $4200 at the rate of 6% simple interest per annum. If he paid an amount of $6468 to clear the loan, then find the time period of the loan.

(8) Jennifer had to pay $3445 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(9) Thomas took a loan of $5600 at the rate of 9% simple interest per annum. If he paid an amount of $9632 to clear the loan, then find the time period of the loan.

(10) What amount does Jennifer have to pay after 6 years if he takes a loan of $3250 at 3% simple interest?