Simple Interest
Math MCQs

Question :    Susan had to pay $4197.5 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  $3650

Solution & Explanation

Solution

Given,

Amount (A) = $4197.5

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

$4197.5 = P (1 + 5% × 3)

⇒ $4197.5 = P (1 + ⁵/₁₀₀ × 3)

⇒ $4197.5 = P (1 + ^{5 × 3}/₁₀₀)

⇒ $4197.5 = P (1 + ¹⁵/₁₀₀)

⇒ $4197.5 = P (^{100 + 15}/₁₀₀)

⇒ $4197.5 = P × ¹¹⁵/₁₀₀

⇒ P × ¹¹⁵/₁₀₀ = $4197.5

⇒ P = ^4197.5/_¹¹⁵/100

⇒ P = 4197.5 × ¹⁰⁰/₁₁₅

⇒ P = ^{4197.5 × 100}/₁₁₅

⇒ P = ⁴¹⁹⁷⁵⁰/₁₁₅

⇒ P = $3650

Thus, the sum borrowed (P) = $3650 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 4197.5, then the Principal = ¹⁰⁰/₁₁₅ × 4197.5

= ^{100 × 4197.5}/₁₁₅

= ⁴¹⁹⁷⁵⁰/₁₁₅

= 3650

Thus, Principal = $3650

Thus, the sum borrowed = $3650 Answer

Similar Questions

(1) Richard took a loan of $5200 at the rate of 7% simple interest per annum. If he paid an amount of $7384 to clear the loan, then find the time period of the loan.

(2) James took a loan of $4000 at the rate of 7% simple interest per annum. If he paid an amount of $5680 to clear the loan, then find the time period of the loan.

(3) John took a loan of $4400 at the rate of 7% simple interest per annum. If he paid an amount of $6864 to clear the loan, then find the time period of the loan.

(4) Emily had to pay $5320 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(5) Find the amount to be paid if Christopher borrowed a sum of $6000 at 3% simple interest for 7 years.

(6) William took a loan of $5000 at the rate of 7% simple interest per annum. If he paid an amount of $7450 to clear the loan, then find the time period of the loan.

(7) Mary took a loan of $4100 at the rate of 10% simple interest per annum. If he paid an amount of $7790 to clear the loan, then find the time period of the loan.

(8) Richard took a loan of $5200 at the rate of 7% simple interest per annum. If he paid an amount of $8476 to clear the loan, then find the time period of the loan.

(9) What amount will be due after 2 years if Thomas borrowed a sum of $3400 at a 10% simple interest?

(10) How much loan did Joshua borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7590 to clear it?