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) Margaret took a loan of $6700 at the rate of 9% simple interest per annum. If he paid an amount of $12127 to clear the loan, then find the time period of the loan.

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

(3) How much loan did James borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $5750 to clear it?

(4) How much loan did John borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $5980 to clear it?

(5) Michelle had to pay $5692.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(6) Find the amount to be paid if Robert borrowed a sum of $5100 at 5% simple interest for 7 years.

(7) Calculate the amount due if Jessica borrowed a sum of $3750 at 5% simple interest for 4 years.

(8) What amount does Jessica have to pay after 5 years if he takes a loan of $3750 at 8% simple interest?

(9) Find the amount to be paid if John borrowed a sum of $5200 at 3% simple interest for 8 years.

(10) James took a loan of $4000 at the rate of 6% simple interest per annum. If he paid an amount of $6160 to clear the loan, then find the time period of the loan.