Simple Interest
Math MCQs

Question :    Jessica had to pay $4312.5 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  $3750

Solution & Explanation

Solution

Given,

Amount (A) = $4312.5

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

$4312.5 = P (1 + 5% × 3)

⇒ $4312.5 = P (1 + ⁵/₁₀₀ × 3)

⇒ $4312.5 = P (1 + ^{5 × 3}/₁₀₀)

⇒ $4312.5 = P (1 + ¹⁵/₁₀₀)

⇒ $4312.5 = P (^{100 + 15}/₁₀₀)

⇒ $4312.5 = P × ¹¹⁵/₁₀₀

⇒ P × ¹¹⁵/₁₀₀ = $4312.5

⇒ P = ^4312.5/_¹¹⁵/100

⇒ P = 4312.5 × ¹⁰⁰/₁₁₅

⇒ P = ^{4312.5 × 100}/₁₁₅

⇒ P = ⁴³¹²⁵⁰/₁₁₅

⇒ P = $3750

Thus, the sum borrowed (P) = $3750 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 4312.5, then the Principal = ¹⁰⁰/₁₁₅ × 4312.5

= ^{100 × 4312.5}/₁₁₅

= ⁴³¹²⁵⁰/₁₁₅

= 3750

Thus, Principal = $3750

Thus, the sum borrowed = $3750 Answer

Similar Questions

(1) Calculate the amount due after 10 years if Charles borrowed a sum of $5900 at a rate of 3% simple interest.

(2) Richard took a loan of $5200 at the rate of 9% simple interest per annum. If he paid an amount of $8476 to clear the loan, then find the time period of the loan.

(3) What amount will be due after 2 years if Joseph borrowed a sum of $3350 at a 6% simple interest?

(4) Find the amount to be paid if Charles borrowed a sum of $5900 at 3% simple interest for 7 years.

(5) John took a loan of $4400 at the rate of 6% simple interest per annum. If he paid an amount of $6512 to clear the loan, then find the time period of the loan.

(6) If Donna paid $5820 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(7) What amount will be due after 2 years if Christopher borrowed a sum of $3500 at a 4% simple interest?

(8) Mary took a loan of $4100 at the rate of 8% simple interest per annum. If he paid an amount of $6396 to clear the loan, then find the time period of the loan.

(9) William took a loan of $5000 at the rate of 8% simple interest per annum. If he paid an amount of $7400 to clear the loan, then find the time period of the loan.

(10) Mary had to pay $3416 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.