Simple Interest
Math MCQs

Question :    How much loan did Kenneth borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8050 to clear it?

Correct Answer  $7000

Solution & Explanation

Solution

Given,

Amount (A) = $8050

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

$8050 = P (1 + 3% × 5)

⇒ $8050 = P (1 + ³/₁₀₀ × 5)

⇒ $8050 = P (1 + ^{3 × 5}/₁₀₀)

⇒ $8050 = P (1 + ¹⁵/₁₀₀)

⇒ $8050 = P (^{100 + 15}/₁₀₀)

⇒ $8050 = P × ¹¹⁵/₁₀₀

⇒ P × ¹¹⁵/₁₀₀ = $8050

⇒ P = ⁸⁰⁵⁰/_¹¹⁵/100

⇒ P = 8050 × ¹⁰⁰/₁₁₅

⇒ P = ^{8050 × 100}/₁₁₅

⇒ P = ⁸⁰⁵⁰⁰⁰/₁₁₅

⇒ P = $7000

Thus, the sum borrowed (P) = $7000 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 8050, then the Principal = ¹⁰⁰/₁₁₅ × 8050

= ^{100 × 8050}/₁₁₅

= ⁸⁰⁵⁰⁰⁰/₁₁₅

= 7000

Thus, Principal = $7000

Thus, the sum borrowed = $7000 Answer

Similar Questions

(1) How much loan did Stephanie borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8682.5 to clear it?

(2) Find the amount to be paid if Susan borrowed a sum of $5650 at 5% simple interest for 8 years.

(3) If Donald paid $4860 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(4) Calculate the amount due if Sarah borrowed a sum of $3850 at 6% simple interest for 4 years.

(5) Daniel took a loan of $6200 at the rate of 10% simple interest per annum. If he paid an amount of $11160 to clear the loan, then find the time period of the loan.

(6) Find the amount to be paid if Jessica borrowed a sum of $5750 at 7% simple interest for 8 years.

(7) How much loan did Steven borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8250 to clear it?

(8) What amount does Mary have to pay after 6 years if he takes a loan of $3050 at 3% simple interest?

(9) How much loan did Joseph borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6840 to clear it?

(10) What amount does Thomas have to pay after 6 years if he takes a loan of $3800 at 8% simple interest?