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) Find the amount to be paid if Susan borrowed a sum of $5650 at 6% simple interest for 8 years.

(2) Michael took a loan of $4600 at the rate of 10% simple interest per annum. If he paid an amount of $8740 to clear the loan, then find the time period of the loan.

(3) Betty took a loan of $6500 at the rate of 7% simple interest per annum. If he paid an amount of $11050 to clear the loan, then find the time period of the loan.

(4) Patricia took a loan of $4300 at the rate of 10% simple interest per annum. If he paid an amount of $6880 to clear the loan, then find the time period of the loan.

(5) Jessica took a loan of $5500 at the rate of 8% simple interest per annum. If he paid an amount of $9020 to clear the loan, then find the time period of the loan.

(6) What amount does Patricia have to pay after 5 years if he takes a loan of $3150 at 8% simple interest?

(7) What amount does Thomas have to pay after 6 years if he takes a loan of $3800 at 3% simple interest?

(8) Calculate the amount due if Robert borrowed a sum of $3100 at 4% simple interest for 4 years.

(9) Calculate the amount due after 10 years if David borrowed a sum of $5400 at a rate of 3% simple interest.

(10) How much loan did Deborah borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8195 to clear it?