Simple Interest
Math MCQs

Question :    Mark had to pay $5060 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  $4400

Solution & Explanation

Solution

Given,

Amount (A) = $5060

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

$5060 = P (1 + 5% × 3)

⇒ $5060 = P (1 + ⁵/₁₀₀ × 3)

⇒ $5060 = P (1 + ^{5 × 3}/₁₀₀)

⇒ $5060 = P (1 + ¹⁵/₁₀₀)

⇒ $5060 = P (^{100 + 15}/₁₀₀)

⇒ $5060 = P × ¹¹⁵/₁₀₀

⇒ P × ¹¹⁵/₁₀₀ = $5060

⇒ P = ⁵⁰⁶⁰/_¹¹⁵/100

⇒ P = 5060 × ¹⁰⁰/₁₁₅

⇒ P = ^{5060 × 100}/₁₁₅

⇒ P = ⁵⁰⁶⁰⁰⁰/₁₁₅

⇒ P = $4400

Thus, the sum borrowed (P) = $4400 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 5060, then the Principal = ¹⁰⁰/₁₁₅ × 5060

= ^{100 × 5060}/₁₁₅

= ⁵⁰⁶⁰⁰⁰/₁₁₅

= 4400

Thus, Principal = $4400

Thus, the sum borrowed = $4400 Answer

Similar Questions

(1) Jessica took a loan of $5500 at the rate of 6% simple interest per annum. If he paid an amount of $8800 to clear the loan, then find the time period of the loan.

(2) Find the amount to be paid if David borrowed a sum of $5400 at 6% simple interest for 8 years.

(3) What amount will be due after 2 years if Michael borrowed a sum of $3150 at a 5% simple interest?

(4) Mark took a loan of $6800 at the rate of 8% simple interest per annum. If he paid an amount of $11152 to clear the loan, then find the time period of the loan.

(5) Find the amount to be paid if Jessica borrowed a sum of $5750 at 10% simple interest for 7 years.

(6) Thomas took a loan of $5600 at the rate of 6% simple interest per annum. If he paid an amount of $8960 to clear the loan, then find the time period of the loan.

(7) Sandra had to pay $4850.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(8) What amount does Joseph have to pay after 5 years if he takes a loan of $3700 at 3% simple interest?

(9) Calculate the amount due if Linda borrowed a sum of $3350 at 2% simple interest for 3 years.

(10) Jessica took a loan of $5500 at the rate of 7% simple interest per annum. If he paid an amount of $8580 to clear the loan, then find the time period of the loan.