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) What amount will be due after 2 years if Joshua borrowed a sum of $3950 at a 6% simple interest?

(2) Calculate the amount due if Linda borrowed a sum of $3350 at 8% simple interest for 4 years.

(3) Joseph took a loan of $5400 at the rate of 9% simple interest per annum. If he paid an amount of $8802 to clear the loan, then find the time period of the loan.

(4) Sarah took a loan of $5700 at the rate of 9% simple interest per annum. If he paid an amount of $9804 to clear the loan, then find the time period of the loan.

(5) Elizabeth took a loan of $4900 at the rate of 8% simple interest per annum. If he paid an amount of $7252 to clear the loan, then find the time period of the loan.

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

(7) How much loan did Susan borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7062.5 to clear it?

(8) Jennifer took a loan of $4500 at the rate of 10% simple interest per annum. If he paid an amount of $7650 to clear the loan, then find the time period of the loan.

(9) Calculate the amount due if Mary borrowed a sum of $3050 at 10% simple interest for 3 years.

(10) What amount will be due after 2 years if John borrowed a sum of $3100 at a 4% simple interest?