Simple Interest
Math MCQs

Question :    David had to pay $3910 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  $3400

Solution & Explanation

Solution

Given,

Amount (A) = $3910

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

$3910 = P (1 + 5% × 3)

⇒ $3910 = P (1 + ⁵/₁₀₀ × 3)

⇒ $3910 = P (1 + ^{5 × 3}/₁₀₀)

⇒ $3910 = P (1 + ¹⁵/₁₀₀)

⇒ $3910 = P (^{100 + 15}/₁₀₀)

⇒ $3910 = P × ¹¹⁵/₁₀₀

⇒ P × ¹¹⁵/₁₀₀ = $3910

⇒ P = ³⁹¹⁰/_¹¹⁵/100

⇒ P = 3910 × ¹⁰⁰/₁₁₅

⇒ P = ^{3910 × 100}/₁₁₅

⇒ P = ³⁹¹⁰⁰⁰/₁₁₅

⇒ P = $3400

Thus, the sum borrowed (P) = $3400 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 3910, then the Principal = ¹⁰⁰/₁₁₅ × 3910

= ^{100 × 3910}/₁₁₅

= ³⁹¹⁰⁰⁰/₁₁₅

= 3400

Thus, Principal = $3400

Thus, the sum borrowed = $3400 Answer

Similar Questions

(1) In how much time a principal of $3050 will amount to $3233 at a simple interest of 3% per annum?

(2) In how much time a principal of $3150 will amount to $3339 at a simple interest of 2% per annum?

(3) Calculate the amount due after 10 years if Jennifer borrowed a sum of $5250 at a rate of 6% simple interest.

(4) David took a loan of $4800 at the rate of 6% simple interest per annum. If he paid an amount of $6816 to clear the loan, then find the time period of the loan.

(5) Elizabeth took a loan of $4900 at the rate of 9% simple interest per annum. If he paid an amount of $8428 to clear the loan, then find the time period of the loan.

(6) How much loan did Sandra borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7740 to clear it?

(7) What amount does Robert have to pay after 6 years if he takes a loan of $3100 at 5% simple interest?

(8) Calculate the amount due if Thomas borrowed a sum of $3800 at 10% simple interest for 3 years.

(9) Emily had to pay $5177.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(10) Calculate the amount due after 10 years if Mary borrowed a sum of $5050 at a rate of 7% simple interest.