Simple Interest
Math MCQs

Question :    How much loan did Linda borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6152.5 to clear it?

Correct Answer  $5350

Solution & Explanation

Solution

Given,

Amount (A) = $6152.5

Rate of Simple Interest (R) = 3%

Time (T) = 5 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

$6152.5 = P (1 + 3% × 5)

⇒ $6152.5 = P (1 + ³/₁₀₀ × 5)

⇒ $6152.5 = P (1 + ^{3 × 5}/₁₀₀)

⇒ $6152.5 = P (1 + ¹⁵/₁₀₀)

⇒ $6152.5 = P (^{100 + 15}/₁₀₀)

⇒ $6152.5 = P × ¹¹⁵/₁₀₀

⇒ P × ¹¹⁵/₁₀₀ = $6152.5

⇒ P = ^6152.5/_¹¹⁵/100

⇒ P = 6152.5 × ¹⁰⁰/₁₁₅

⇒ P = ^{6152.5 × 100}/₁₁₅

⇒ P = ⁶¹⁵²⁵⁰/₁₁₅

⇒ P = $5350

Thus, the sum borrowed (P) = $5350 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 = 5 years

So, we need to calculate the simple interest for the given time period, which is 5 years

Thus, Simple Interest for 5 years = 5 × Simple Interest for 1 year

= 5 × 3 = 15

Thus, simple interest for 5 years = 15

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 15 = 115

Calculation of the Principal

Now,

∵ If the Amount is 115, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₁₅

∴ If the Amount is 6152.5, then the Principal = ¹⁰⁰/₁₁₅ × 6152.5

= ^{100 × 6152.5}/₁₁₅

= ⁶¹⁵²⁵⁰/₁₁₅

= 5350

Thus, Principal = $5350

Thus, the sum borrowed = $5350 Answer

Similar Questions

(1) Thomas had to pay $4028 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(2) If William paid $3920 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(3) Robert took a loan of $4200 at the rate of 6% simple interest per annum. If he paid an amount of $6720 to clear the loan, then find the time period of the loan.

(4) Susan took a loan of $5300 at the rate of 6% simple interest per annum. If he paid an amount of $8162 to clear the loan, then find the time period of the loan.

(5) Calculate the amount due if Sarah borrowed a sum of $3850 at 9% simple interest for 4 years.

(6) Calculate the amount due after 9 years if Mary borrowed a sum of $5050 at a rate of 5% simple interest.

(7) If Barbara paid $3834 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(8) What amount will be due after 2 years if Joshua borrowed a sum of $3950 at a 9% simple interest?

(9) Calculate the amount due after 10 years if Thomas borrowed a sum of $5800 at a rate of 8% simple interest.

(10) What amount will be due after 2 years if William borrowed a sum of $3250 at a 6% simple interest?