Simple Interest
Math MCQs

Question :    If Richard paid $4032 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

Correct Answer  $3600

Solution & Explanation

Solution

Given,

Amount (A) = $4032

Rate of Simple Interest (R) = 3%

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

$4032 = P (1 + 3% × 4)

⇒ $4032 = P (1 + ³/₁₀₀ × 4)

⇒ $4032 = P (1 + ^{3 × 4}/₁₀₀)

⇒ $4032 = P (1 + ¹²/₁₀₀)

⇒ $4032 = P (^{100 + 12}/₁₀₀)

⇒ $4032 = P × ¹¹²/₁₀₀

⇒ P × ¹¹²/₁₀₀ = $4032

⇒ P = ⁴⁰³²/_¹¹²/100

⇒ P = 4032 × ¹⁰⁰/₁₁₂

⇒ P = ^{4032 × 100}/₁₁₂

⇒ P = ⁴⁰³²⁰⁰/₁₁₂

⇒ P = $3600

Thus, the sum borrowed (P) = $3600 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 = 3% per annum

Thus, Interest = 3% of principal

⇒ Interest = 3% of 100 = 3

Thus, Simple Interest for 1 year = 3

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 × 3 = 12

Thus, simple interest for 4 years = 12

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 12 = 112

Calculation of the Principal

Now,

∵ If the Amount is 112, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₁₂

∴ If the Amount is 4032, then the Principal = ¹⁰⁰/₁₁₂ × 4032

= ^{100 × 4032}/₁₁₂

= ⁴⁰³²⁰⁰/₁₁₂

= 3600

Thus, Principal = $3600

Thus, the sum borrowed = $3600 Answer

Similar Questions

(1) David took a loan of $4800 at the rate of 10% simple interest per annum. If he paid an amount of $8640 to clear the loan, then find the time period of the loan.

(2) If David paid $3808 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(3) What amount will be due after 2 years if Joshua borrowed a sum of $3950 at a 10% simple interest?

(4) What amount does Jennifer have to pay after 5 years if he takes a loan of $3250 at 3% simple interest?

(5) If Susan borrowed $3650 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.

(6) Thomas had to pay $4256 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(7) Christopher took a loan of $6000 at the rate of 8% simple interest per annum. If he paid an amount of $8880 to clear the loan, then find the time period of the loan.

(8) What amount will be due after 2 years if Andrew borrowed a sum of $3900 at a 7% simple interest?

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

(10) How much loan did Dorothy borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9062.5 to clear it?