Simple Interest
Math MCQs

Question :    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?

Correct Answer  $5000

Solution & Explanation

Solution

Given,

Amount (A) = $5750

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

$5750 = P (1 + 3% × 5)

⇒ $5750 = P (1 + ³/₁₀₀ × 5)

⇒ $5750 = P (1 + ^{3 × 5}/₁₀₀)

⇒ $5750 = P (1 + ¹⁵/₁₀₀)

⇒ $5750 = P (^{100 + 15}/₁₀₀)

⇒ $5750 = P × ¹¹⁵/₁₀₀

⇒ P × ¹¹⁵/₁₀₀ = $5750

⇒ P = ⁵⁷⁵⁰/_¹¹⁵/100

⇒ P = 5750 × ¹⁰⁰/₁₁₅

⇒ P = ^{5750 × 100}/₁₁₅

⇒ P = ⁵⁷⁵⁰⁰⁰/₁₁₅

⇒ P = $5000

Thus, the sum borrowed (P) = $5000 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 5750, then the Principal = ¹⁰⁰/₁₁₅ × 5750

= ^{100 × 5750}/₁₁₅

= ⁵⁷⁵⁰⁰⁰/₁₁₅

= 5000

Thus, Principal = $5000

Thus, the sum borrowed = $5000 Answer

Similar Questions

(1) Calculate the amount due after 10 years if Karen borrowed a sum of $5950 at a rate of 3% simple interest.

(2) How much loan did Timothy borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8510 to clear it?

(3) Find the amount to be paid if Joseph borrowed a sum of $5700 at 10% simple interest for 8 years.

(4) What amount will be due after 2 years if Mark borrowed a sum of $3700 at a 4% simple interest?

(5) Jennifer took a loan of $4500 at the rate of 10% simple interest per annum. If he paid an amount of $9000 to clear the loan, then find the time period of the loan.

(6) Calculate the amount due if David borrowed a sum of $3400 at 9% simple interest for 4 years.

(7) Find the amount to be paid if Jessica borrowed a sum of $5750 at 9% simple interest for 7 years.

(8) What amount does Mary have to pay after 5 years if he takes a loan of $3050 at 9% simple interest?

(9) Kenneth had to pay $5300 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(10) What amount will be due after 2 years if Matthew borrowed a sum of $3600 at a 10% simple interest?