Simple Interest
Math MCQs

Question :    Daniel had to pay $4346 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  $4100

Solution & Explanation

Solution

Given,

Amount (A) = $4346

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

$4346 = P (1 + 2% × 3)

⇒ $4346 = P (1 + ²/₁₀₀ × 3)

⇒ $4346 = P (1 + ^{2 × 3}/₁₀₀)

⇒ $4346 = P (1 + ⁶/₁₀₀)

⇒ $4346 = P (^{100 + 6}/₁₀₀)

⇒ $4346 = P × ¹⁰⁶/₁₀₀

⇒ P × ¹⁰⁶/₁₀₀ = $4346

⇒ P = ⁴³⁴⁶/_¹⁰⁶/100

⇒ P = 4346 × ¹⁰⁰/₁₀₆

⇒ P = ^{4346 × 100}/₁₀₆

⇒ P = ⁴³⁴⁶⁰⁰/₁₀₆

⇒ P = $4100

Thus, the sum borrowed (P) = $4100 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 4346, then the Principal = ¹⁰⁰/₁₀₆ × 4346

= ^{100 × 4346}/₁₀₆

= ⁴³⁴⁶⁰⁰/₁₀₆

= 4100

Thus, Principal = $4100

Thus, the sum borrowed = $4100 Answer

Similar Questions

(1) Elizabeth took a loan of $4900 at the rate of 7% simple interest per annum. If he paid an amount of $8330 to clear the loan, then find the time period of the loan.

(2) Calculate the amount due if Christopher borrowed a sum of $4000 at 6% simple interest for 4 years.

(3) Sandra took a loan of $6900 at the rate of 7% simple interest per annum. If he paid an amount of $10281 to clear the loan, then find the time period of the loan.

(4) Calculate the amount due if Jennifer borrowed a sum of $3250 at 7% simple interest for 4 years.

(5) What amount does Jessica have to pay after 5 years if he takes a loan of $3750 at 4% simple interest?

(6) Find the amount to be paid if Robert borrowed a sum of $5100 at 7% simple interest for 8 years.

(7) Calculate the amount due if Thomas borrowed a sum of $3800 at 3% simple interest for 3 years.

(8) What amount does Jessica have to pay after 5 years if he takes a loan of $3750 at 3% simple interest?

(9) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 2% simple interest?

(10) How much loan did Jason borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8855 to clear it?