Simple Interest
Math MCQs

Question :    Paul had to pay $5405 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  $4700

Solution & Explanation

Solution

Given,

Amount (A) = $5405

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

$5405 = P (1 + 5% × 3)

⇒ $5405 = P (1 + ⁵/₁₀₀ × 3)

⇒ $5405 = P (1 + ^{5 × 3}/₁₀₀)

⇒ $5405 = P (1 + ¹⁵/₁₀₀)

⇒ $5405 = P (^{100 + 15}/₁₀₀)

⇒ $5405 = P × ¹¹⁵/₁₀₀

⇒ P × ¹¹⁵/₁₀₀ = $5405

⇒ P = ⁵⁴⁰⁵/_¹¹⁵/100

⇒ P = 5405 × ¹⁰⁰/₁₁₅

⇒ P = ^{5405 × 100}/₁₁₅

⇒ P = ⁵⁴⁰⁵⁰⁰/₁₁₅

⇒ P = $4700

Thus, the sum borrowed (P) = $4700 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 5405, then the Principal = ¹⁰⁰/₁₁₅ × 5405

= ^{100 × 5405}/₁₁₅

= ⁵⁴⁰⁵⁰⁰/₁₁₅

= 4700

Thus, Principal = $4700

Thus, the sum borrowed = $4700 Answer

Similar Questions

(1) Joshua had to pay $5341 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(2) What amount will be due after 2 years if Kenneth borrowed a sum of $4000 at a 8% simple interest?

(3) What amount does Mary have to pay after 5 years if he takes a loan of $3050 at 6% simple interest?

(4) Lisa took a loan of $6100 at the rate of 10% simple interest per annum. If he paid an amount of $10980 to clear the loan, then find the time period of the loan.

(5) What amount does Jennifer have to pay after 6 years if he takes a loan of $3250 at 8% simple interest?

(6) Donna had to pay $5577.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(7) Margaret had to pay $4872 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(8) Richard took a loan of $5200 at the rate of 10% simple interest per annum. If he paid an amount of $8320 to clear the loan, then find the time period of the loan.

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

(10) Barbara had to pay $4082.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.