Simple Interest
Math MCQs

Question :    Christopher had to pay $4600 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  $4000

Solution & Explanation

Solution

Given,

Amount (A) = $4600

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

$4600 = P (1 + 5% × 3)

⇒ $4600 = P (1 + ⁵/₁₀₀ × 3)

⇒ $4600 = P (1 + ^{5 × 3}/₁₀₀)

⇒ $4600 = P (1 + ¹⁵/₁₀₀)

⇒ $4600 = P (^{100 + 15}/₁₀₀)

⇒ $4600 = P × ¹¹⁵/₁₀₀

⇒ P × ¹¹⁵/₁₀₀ = $4600

⇒ P = ⁴⁶⁰⁰/_¹¹⁵/100

⇒ P = 4600 × ¹⁰⁰/₁₁₅

⇒ P = ^{4600 × 100}/₁₁₅

⇒ P = ⁴⁶⁰⁰⁰⁰/₁₁₅

⇒ P = $4000

Thus, the sum borrowed (P) = $4000 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 4600, then the Principal = ¹⁰⁰/₁₁₅ × 4600

= ^{100 × 4600}/₁₁₅

= ⁴⁶⁰⁰⁰⁰/₁₁₅

= 4000

Thus, Principal = $4000

Thus, the sum borrowed = $4000 Answer

Similar Questions

(1) Susan took a loan of $5300 at the rate of 7% simple interest per annum. If he paid an amount of $8639 to clear the loan, then find the time period of the loan.

(2) What amount does Linda have to pay after 6 years if he takes a loan of $3350 at 2% simple interest?

(3) Calculate the amount due if Mary borrowed a sum of $3050 at 7% simple interest for 3 years.

(4) Calculate the amount due if Charles borrowed a sum of $3900 at 4% simple interest for 4 years.

(5) Calculate the amount due after 10 years if Richard borrowed a sum of $5600 at a rate of 2% simple interest.

(6) What amount does Linda have to pay after 6 years if he takes a loan of $3350 at 9% simple interest?

(7) Find the amount to be paid if Mary borrowed a sum of $5050 at 9% simple interest for 7 years.

(8) Charles took a loan of $5800 at the rate of 8% simple interest per annum. If he paid an amount of $9976 to clear the loan, then find the time period of the loan.

(9) Susan took a loan of $5300 at the rate of 7% simple interest per annum. If he paid an amount of $9010 to clear the loan, then find the time period of the loan.

(10) Calculate the amount due if David borrowed a sum of $3400 at 10% simple interest for 3 years.