Simple Interest
Math MCQs

Question :    Emily had to pay $5035 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

Correct Answer  $4750

Solution & Explanation

Solution

Given,

Amount (A) = $5035

Rate of Simple Interest (R) = 2%

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

$5035 = P (1 + 2% × 3)

⇒ $5035 = P (1 + ²/₁₀₀ × 3)

⇒ $5035 = P (1 + ^{2 × 3}/₁₀₀)

⇒ $5035 = P (1 + ⁶/₁₀₀)

⇒ $5035 = P (^{100 + 6}/₁₀₀)

⇒ $5035 = P × ¹⁰⁶/₁₀₀

⇒ P × ¹⁰⁶/₁₀₀ = $5035

⇒ P = ⁵⁰³⁵/_¹⁰⁶/100

⇒ P = 5035 × ¹⁰⁰/₁₀₆

⇒ P = ^{5035 × 100}/₁₀₆

⇒ P = ⁵⁰³⁵⁰⁰/₁₀₆

⇒ P = $4750

Thus, the sum borrowed (P) = $4750 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 = 2% per annum

Thus, Interest = 2% of principal

⇒ Interest = 2% of 100 = 2

Thus, Simple Interest for 1 year = 2

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 × 2 = 6

Thus, simple interest for 3 years = 6

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 6 = 106

Calculation of the Principal

Now,

∵ If the Amount is 106, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₀₆

∴ If the Amount is 5035, then the Principal = ¹⁰⁰/₁₀₆ × 5035

= ^{100 × 5035}/₁₀₆

= ⁵⁰³⁵⁰⁰/₁₀₆

= 4750

Thus, Principal = $4750

Thus, the sum borrowed = $4750 Answer

Similar Questions

(1) Barbara took a loan of $5100 at the rate of 9% simple interest per annum. If he paid an amount of $9231 to clear the loan, then find the time period of the loan.

(2) What amount does William have to pay after 6 years if he takes a loan of $3500 at 10% simple interest?

(3) In how much time a principal of $3000 will amount to $3300 at a simple interest of 2% per annum?

(4) 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.

(5) What amount does Mary have to pay after 5 years if he takes a loan of $3050 at 9% simple interest?

(6) Find the amount to be paid if Richard borrowed a sum of $5600 at 6% simple interest for 8 years.

(7) Nancy took a loan of $6300 at the rate of 10% simple interest per annum. If he paid an amount of $11340 to clear the loan, then find the time period of the loan.

(8) Elizabeth took a loan of $4900 at the rate of 8% simple interest per annum. If he paid an amount of $7644 to clear the loan, then find the time period of the loan.

(9) How much loan did Sharon borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8912.5 to clear it?

(10) Calculate the amount due if Susan borrowed a sum of $3650 at 9% simple interest for 4 years.