Simple Interest
Math MCQs

Question :    Betty had to pay $4505 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  $4250

Solution & Explanation

Solution

Given,

Amount (A) = $4505

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

$4505 = P (1 + 2% × 3)

⇒ $4505 = P (1 + ²/₁₀₀ × 3)

⇒ $4505 = P (1 + ^{2 × 3}/₁₀₀)

⇒ $4505 = P (1 + ⁶/₁₀₀)

⇒ $4505 = P (^{100 + 6}/₁₀₀)

⇒ $4505 = P × ¹⁰⁶/₁₀₀

⇒ P × ¹⁰⁶/₁₀₀ = $4505

⇒ P = ⁴⁵⁰⁵/_¹⁰⁶/100

⇒ P = 4505 × ¹⁰⁰/₁₀₆

⇒ P = ^{4505 × 100}/₁₀₆

⇒ P = ⁴⁵⁰⁵⁰⁰/₁₀₆

⇒ P = $4250

Thus, the sum borrowed (P) = $4250 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 4505, then the Principal = ¹⁰⁰/₁₀₆ × 4505

= ^{100 × 4505}/₁₀₆

= ⁴⁵⁰⁵⁰⁰/₁₀₆

= 4250

Thus, Principal = $4250

Thus, the sum borrowed = $4250 Answer

Similar Questions

(1) Michael took a loan of $4600 at the rate of 7% simple interest per annum. If he paid an amount of $6854 to clear the loan, then find the time period of the loan.

(2) How much loan did Nancy borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7380 to clear it?

(3) Calculate the amount due after 10 years if Jessica borrowed a sum of $5750 at a rate of 10% simple interest.

(4) What amount does William have to pay after 6 years if he takes a loan of $3500 at 10% simple interest?

(5) Calculate the amount due after 9 years if Christopher borrowed a sum of $6000 at a rate of 6% simple interest.

(6) Donald had to pay $5040 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(7) James took a loan of $4000 at the rate of 8% simple interest per annum. If he paid an amount of $7200 to clear the loan, then find the time period of the loan.

(8) Find the amount to be paid if James borrowed a sum of $5000 at 8% simple interest for 7 years.

(9) Find the amount to be paid if David borrowed a sum of $5400 at 2% simple interest for 7 years.

(10) David took a loan of $4800 at the rate of 9% simple interest per annum. If he paid an amount of $8256 to clear the loan, then find the time period of the loan.