Simple Interest
Math MCQs

Question :    Sarah had to pay $4427.5 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  $3850

Solution & Explanation

Solution

Given,

Amount (A) = $4427.5

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

$4427.5 = P (1 + 5% × 3)

⇒ $4427.5 = P (1 + ⁵/₁₀₀ × 3)

⇒ $4427.5 = P (1 + ^{5 × 3}/₁₀₀)

⇒ $4427.5 = P (1 + ¹⁵/₁₀₀)

⇒ $4427.5 = P (^{100 + 15}/₁₀₀)

⇒ $4427.5 = P × ¹¹⁵/₁₀₀

⇒ P × ¹¹⁵/₁₀₀ = $4427.5

⇒ P = ^4427.5/_¹¹⁵/100

⇒ P = 4427.5 × ¹⁰⁰/₁₁₅

⇒ P = ^{4427.5 × 100}/₁₁₅

⇒ P = ⁴⁴²⁷⁵⁰/₁₁₅

⇒ P = $3850

Thus, the sum borrowed (P) = $3850 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 4427.5, then the Principal = ¹⁰⁰/₁₁₅ × 4427.5

= ^{100 × 4427.5}/₁₁₅

= ⁴⁴²⁷⁵⁰/₁₁₅

= 3850

Thus, Principal = $3850

Thus, the sum borrowed = $3850 Answer

Similar Questions

(1) How much loan did Thomas borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6670 to clear it?

(2) John took a loan of $4400 at the rate of 8% simple interest per annum. If he paid an amount of $7920 to clear the loan, then find the time period of the loan.

(3) Find the amount to be paid if Joseph borrowed a sum of $5700 at 9% simple interest for 8 years.

(4) Betty took a loan of $6500 at the rate of 6% simple interest per annum. If he paid an amount of $10400 to clear the loan, then find the time period of the loan.

(5) Elizabeth took a loan of $4900 at the rate of 8% simple interest per annum. If he paid an amount of $8428 to clear the loan, then find the time period of the loan.

(6) Christopher took a loan of $6000 at the rate of 8% simple interest per annum. If he paid an amount of $9360 to clear the loan, then find the time period of the loan.

(7) Sarah took a loan of $5700 at the rate of 10% simple interest per annum. If he paid an amount of $10260 to clear the loan, then find the time period of the loan.

(8) Mary took a loan of $4100 at the rate of 7% simple interest per annum. If he paid an amount of $6683 to clear the loan, then find the time period of the loan.

(9) Find the amount to be paid if Mary borrowed a sum of $5050 at 10% simple interest for 8 years.

(10) In how much time a principal of $3050 will amount to $3660 at a simple interest of 4% per annum?