Simple Interest
Math MCQs

Question :    James had to pay $3450 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

Correct Answer  $3000

Solution & Explanation

Solution

Given,

Amount (A) = $3450

Rate of Simple Interest (R) = 5%

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

$3450 = P (1 + 5% × 3)

⇒ $3450 = P (1 + ⁵/₁₀₀ × 3)

⇒ $3450 = P (1 + ^{5 × 3}/₁₀₀)

⇒ $3450 = P (1 + ¹⁵/₁₀₀)

⇒ $3450 = P (^{100 + 15}/₁₀₀)

⇒ $3450 = P × ¹¹⁵/₁₀₀

⇒ P × ¹¹⁵/₁₀₀ = $3450

⇒ P = ³⁴⁵⁰/_¹¹⁵/100

⇒ P = 3450 × ¹⁰⁰/₁₁₅

⇒ P = ^{3450 × 100}/₁₁₅

⇒ P = ³⁴⁵⁰⁰⁰/₁₁₅

⇒ P = $3000

Thus, the sum borrowed (P) = $3000 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 = 5% per annum

Thus, Interest = 5% of principal

⇒ Interest = 5% of 100 = 5

Thus, Simple Interest for 1 year = 5

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 × 5 = 15

Thus, simple interest for 3 years = 15

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 15 = 115

Calculation of the Principal

Now,

∵ If the Amount is 115, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₁₅

∴ If the Amount is 3450, then the Principal = ¹⁰⁰/₁₁₅ × 3450

= ^{100 × 3450}/₁₁₅

= ³⁴⁵⁰⁰⁰/₁₁₅

= 3000

Thus, Principal = $3000

Thus, the sum borrowed = $3000 Answer

Similar Questions

(1) Jessica took a loan of $5500 at the rate of 8% simple interest per annum. If he paid an amount of $9460 to clear the loan, then find the time period of the loan.

(2) James took a loan of $4000 at the rate of 9% simple interest per annum. If he paid an amount of $6880 to clear the loan, then find the time period of the loan.

(3) Christopher took a loan of $6000 at the rate of 8% simple interest per annum. If he paid an amount of $9840 to clear the loan, then find the time period of the loan.

(4) Robert had to pay $3565 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(5) Linda took a loan of $4700 at the rate of 8% simple interest per annum. If he paid an amount of $8084 to clear the loan, then find the time period of the loan.

(6) Calculate the amount due after 9 years if Patricia borrowed a sum of $5150 at a rate of 6% simple interest.

(7) Sarah took a loan of $5700 at the rate of 7% simple interest per annum. If he paid an amount of $8493 to clear the loan, then find the time period of the loan.

(8) What amount does Christopher have to pay after 6 years if he takes a loan of $4000 at 3% simple interest?

(9) What amount does Elizabeth have to pay after 6 years if he takes a loan of $3450 at 4% simple interest?

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