Simple Interest
Math MCQs

Question :    Jennifer had to pay $3445 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  $3250

Solution & Explanation

Solution

Given,

Amount (A) = $3445

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

$3445 = P (1 + 2% × 3)

⇒ $3445 = P (1 + ²/₁₀₀ × 3)

⇒ $3445 = P (1 + ^{2 × 3}/₁₀₀)

⇒ $3445 = P (1 + ⁶/₁₀₀)

⇒ $3445 = P (^{100 + 6}/₁₀₀)

⇒ $3445 = P × ¹⁰⁶/₁₀₀

⇒ P × ¹⁰⁶/₁₀₀ = $3445

⇒ P = ³⁴⁴⁵/_¹⁰⁶/100

⇒ P = 3445 × ¹⁰⁰/₁₀₆

⇒ P = ^{3445 × 100}/₁₀₆

⇒ P = ³⁴⁴⁵⁰⁰/₁₀₆

⇒ P = $3250

Thus, the sum borrowed (P) = $3250 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 3445, then the Principal = ¹⁰⁰/₁₀₆ × 3445

= ^{100 × 3445}/₁₀₆

= ³⁴⁴⁵⁰⁰/₁₀₆

= 3250

Thus, Principal = $3250

Thus, the sum borrowed = $3250 Answer

Similar Questions

(1) Anthony took a loan of $6600 at the rate of 7% simple interest per annum. If he paid an amount of $11220 to clear the loan, then find the time period of the loan.

(2) Barbara took a loan of $5100 at the rate of 7% simple interest per annum. If he paid an amount of $8313 to clear the loan, then find the time period of the loan.

(3) Jessica took a loan of $5500 at the rate of 9% simple interest per annum. If he paid an amount of $8470 to clear the loan, then find the time period of the loan.

(4) Calculate the amount due if Robert borrowed a sum of $3100 at 10% simple interest for 4 years.

(5) What amount does Jennifer have to pay after 5 years if he takes a loan of $3250 at 8% simple interest?

(6) Linda took a loan of $4700 at the rate of 7% simple interest per annum. If he paid an amount of $7661 to clear the loan, then find the time period of the loan.

(7) Find the amount to be paid if Michael borrowed a sum of $5300 at 4% simple interest for 8 years.

(8) What amount does Sarah have to pay after 5 years if he takes a loan of $3850 at 6% simple interest?

(9) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 3% simple interest for 7 years.

(10) Nancy took a loan of $6300 at the rate of 6% simple interest per annum. If he paid an amount of $9702 to clear the loan, then find the time period of the loan.