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) How much loan did Patricia borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5665 to clear it?

(2) Barbara took a loan of $5100 at the rate of 8% simple interest per annum. If he paid an amount of $7956 to clear the loan, then find the time period of the loan.

(3) What amount does Elizabeth have to pay after 5 years if he takes a loan of $3450 at 10% simple interest?

(4) Calculate the amount due if Jennifer borrowed a sum of $3250 at 6% simple interest for 3 years.

(5) If Jessica paid $4350 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(6) Calculate the amount due after 9 years if Christopher borrowed a sum of $6000 at a rate of 3% simple interest.

(7) Margaret took a loan of $6700 at the rate of 10% simple interest per annum. If he paid an amount of $13400 to clear the loan, then find the time period of the loan.

(8) Joseph took a loan of $5400 at the rate of 8% simple interest per annum. If he paid an amount of $8424 to clear the loan, then find the time period of the loan.

(9) Sandra had to pay $4984 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(10) Richard took a loan of $5200 at the rate of 10% simple interest per annum. If he paid an amount of $9360 to clear the loan, then find the time period of the loan.