Simple Interest
Math MCQs

Question :    Joseph had to pay $4255 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

Correct Answer  $3700

Solution & Explanation

Solution

Given,

Amount (A) = $4255

Rate of Simple Interest (R) = 5%

Time (T) = 3 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

$4255 = P (1 + 5% × 3)

⇒ $4255 = P (1 + ⁵/₁₀₀ × 3)

⇒ $4255 = P (1 + ^{5 × 3}/₁₀₀)

⇒ $4255 = P (1 + ¹⁵/₁₀₀)

⇒ $4255 = P (^{100 + 15}/₁₀₀)

⇒ $4255 = P × ¹¹⁵/₁₀₀

⇒ P × ¹¹⁵/₁₀₀ = $4255

⇒ P = ⁴²⁵⁵/_¹¹⁵/100

⇒ P = 4255 × ¹⁰⁰/₁₁₅

⇒ P = ^{4255 × 100}/₁₁₅

⇒ P = ⁴²⁵⁵⁰⁰/₁₁₅

⇒ P = $3700

Thus, the sum borrowed (P) = $3700 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 = 5% per annum

Thus, Interest = 5% of principal

⇒ Interest = 5% of 100 = 5

Thus, Simple Interest for 1 year = 5

Calculation of the Amount

Since, in the question, time = 3 years

So, we need to calculate the simple interest for the given time period, which is 3 years

Thus, Simple Interest for 3 years = 3 × Simple Interest for 1 year

= 3 × 5 = 15

Thus, simple interest for 3 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 4255, then the Principal = ¹⁰⁰/₁₁₅ × 4255

= ^{100 × 4255}/₁₁₅

= ⁴²⁵⁵⁰⁰/₁₁₅

= 3700

Thus, Principal = $3700

Thus, the sum borrowed = $3700 Answer

Similar Questions

(1) Calculate the amount due after 9 years if Charles borrowed a sum of $5900 at a rate of 5% simple interest.

(2) Karen took a loan of $5900 at the rate of 7% simple interest per annum. If he paid an amount of $10030 to clear the loan, then find the time period of the loan.

(3) Calculate the amount due if James borrowed a sum of $3000 at 5% simple interest for 3 years.

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

(5) William took a loan of $5000 at the rate of 7% simple interest per annum. If he paid an amount of $8150 to clear the loan, then find the time period of the loan.

(6) Find the amount to be paid if Barbara borrowed a sum of $5550 at 7% simple interest for 8 years.

(7) What amount does Michael have to pay after 5 years if he takes a loan of $3300 at 5% simple interest?

(8) What amount does David have to pay after 5 years if he takes a loan of $3400 at 10% simple interest?

(9) What amount does David have to pay after 6 years if he takes a loan of $3400 at 6% simple interest?

(10) What amount does James have to pay after 5 years if he takes a loan of $3000 at 6% simple interest?