Simple Interest
Math MCQs

Question :    Linda had to pay $3551 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  $3350

Solution & Explanation

Solution

Given,

Amount (A) = $3551

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

$3551 = P (1 + 2% × 3)

⇒ $3551 = P (1 + ²/₁₀₀ × 3)

⇒ $3551 = P (1 + ^{2 × 3}/₁₀₀)

⇒ $3551 = P (1 + ⁶/₁₀₀)

⇒ $3551 = P (^{100 + 6}/₁₀₀)

⇒ $3551 = P × ¹⁰⁶/₁₀₀

⇒ P × ¹⁰⁶/₁₀₀ = $3551

⇒ P = ³⁵⁵¹/_¹⁰⁶/100

⇒ P = 3551 × ¹⁰⁰/₁₀₆

⇒ P = ^{3551 × 100}/₁₀₆

⇒ P = ³⁵⁵¹⁰⁰/₁₀₆

⇒ P = $3350

Thus, the sum borrowed (P) = $3350 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 3551, then the Principal = ¹⁰⁰/₁₀₆ × 3551

= ^{100 × 3551}/₁₀₆

= ³⁵⁵¹⁰⁰/₁₀₆

= 3350

Thus, Principal = $3350

Thus, the sum borrowed = $3350 Answer

Similar Questions

(1) Find the amount to be paid if Richard borrowed a sum of $5600 at 9% simple interest for 7 years.

(2) Calculate the amount due if Susan borrowed a sum of $3650 at 3% simple interest for 3 years.

(3) What amount does Michael have to pay after 5 years if he takes a loan of $3300 at 9% simple interest?

(4) William had to pay $4025 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(5) Steven had to pay $4876 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(6) Nancy took a loan of $6300 at the rate of 6% simple interest per annum. If he paid an amount of $10080 to clear the loan, then find the time period of the loan.

(7) What amount does Charles have to pay after 6 years if he takes a loan of $3900 at 10% simple interest?

(8) Barbara took a loan of $5100 at the rate of 8% simple interest per annum. If he paid an amount of $7956 to clear the loan, then find the time period of the loan.

(9) Mark had to pay $5060 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(10) What amount will be due after 2 years if Charles borrowed a sum of $3450 at a 4% simple interest?