Simple Interest
Math MCQs

Question :    Donna had to pay $5141 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  $4850

Solution & Explanation

Solution

Given,

Amount (A) = $5141

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

$5141 = P (1 + 2% × 3)

⇒ $5141 = P (1 + ²/₁₀₀ × 3)

⇒ $5141 = P (1 + ^{2 × 3}/₁₀₀)

⇒ $5141 = P (1 + ⁶/₁₀₀)

⇒ $5141 = P (^{100 + 6}/₁₀₀)

⇒ $5141 = P × ¹⁰⁶/₁₀₀

⇒ P × ¹⁰⁶/₁₀₀ = $5141

⇒ P = ⁵¹⁴¹/_¹⁰⁶/100

⇒ P = 5141 × ¹⁰⁰/₁₀₆

⇒ P = ^{5141 × 100}/₁₀₆

⇒ P = ⁵¹⁴¹⁰⁰/₁₀₆

⇒ P = $4850

Thus, the sum borrowed (P) = $4850 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 5141, then the Principal = ¹⁰⁰/₁₀₆ × 5141

= ^{100 × 5141}/₁₀₆

= ⁵¹⁴¹⁰⁰/₁₀₆

= 4850

Thus, Principal = $4850

Thus, the sum borrowed = $4850 Answer

Similar Questions

(1) Find the amount to be paid if Thomas borrowed a sum of $5800 at 5% simple interest for 8 years.

(2) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 6% simple interest for 7 years.

(3) Find the amount to be paid if Susan borrowed a sum of $5650 at 8% simple interest for 7 years.

(4) Linda had to pay $3752 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(5) What amount will be due after 2 years if Mark borrowed a sum of $3700 at a 4% simple interest?

(6) Matthew took a loan of $6400 at the rate of 8% simple interest per annum. If he paid an amount of $9984 to clear the loan, then find the time period of the loan.

(7) David took a loan of $4800 at the rate of 8% simple interest per annum. If he paid an amount of $7104 to clear the loan, then find the time period of the loan.

(8) Calculate the amount due after 10 years if Elizabeth borrowed a sum of $5450 at a rate of 4% simple interest.

(9) Find the amount to be paid if Patricia borrowed a sum of $5150 at 9% simple interest for 8 years.

(10) What amount does Barbara have to pay after 6 years if he takes a loan of $3550 at 2% simple interest?