Simple Interest
Math MCQs

Question :    Elizabeth had to pay $3657 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  $3450

Solution & Explanation

Solution

Given,

Amount (A) = $3657

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

$3657 = P (1 + 2% × 3)

⇒ $3657 = P (1 + ²/₁₀₀ × 3)

⇒ $3657 = P (1 + ^{2 × 3}/₁₀₀)

⇒ $3657 = P (1 + ⁶/₁₀₀)

⇒ $3657 = P (^{100 + 6}/₁₀₀)

⇒ $3657 = P × ¹⁰⁶/₁₀₀

⇒ P × ¹⁰⁶/₁₀₀ = $3657

⇒ P = ³⁶⁵⁷/_¹⁰⁶/100

⇒ P = 3657 × ¹⁰⁰/₁₀₆

⇒ P = ^{3657 × 100}/₁₀₆

⇒ P = ³⁶⁵⁷⁰⁰/₁₀₆

⇒ P = $3450

Thus, the sum borrowed (P) = $3450 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 3657, then the Principal = ¹⁰⁰/₁₀₆ × 3657

= ^{100 × 3657}/₁₀₆

= ³⁶⁵⁷⁰⁰/₁₀₆

= 3450

Thus, Principal = $3450

Thus, the sum borrowed = $3450 Answer

Similar Questions

(1) Find the amount to be paid if Mary borrowed a sum of $5050 at 5% simple interest for 7 years.

(2) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 2% simple interest for 7 years.

(3) What amount does Elizabeth have to pay after 5 years if he takes a loan of $3450 at 5% simple interest?

(4) Find the amount to be paid if Sarah borrowed a sum of $5850 at 5% simple interest for 8 years.

(5) Lisa took a loan of $6100 at the rate of 6% simple interest per annum. If he paid an amount of $9028 to clear the loan, then find the time period of the loan.

(6) What amount does Karen have to pay after 5 years if he takes a loan of $3950 at 8% simple interest?

(7) Jessica took a loan of $5500 at the rate of 7% simple interest per annum. If he paid an amount of $8580 to clear the loan, then find the time period of the loan.

(8) Find the amount to be paid if Susan borrowed a sum of $5650 at 10% simple interest for 8 years.

(9) If Patricia paid $3402 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(10) Calculate the amount due if Patricia borrowed a sum of $3150 at 8% simple interest for 3 years.