Simple Interest
Math MCQs

Question :    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.

Correct Answer  $3100

Solution & Explanation

Solution

Given,

Amount (A) = $3565

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

$3565 = P (1 + 5% × 3)

⇒ $3565 = P (1 + ⁵/₁₀₀ × 3)

⇒ $3565 = P (1 + ^{5 × 3}/₁₀₀)

⇒ $3565 = P (1 + ¹⁵/₁₀₀)

⇒ $3565 = P (^{100 + 15}/₁₀₀)

⇒ $3565 = P × ¹¹⁵/₁₀₀

⇒ P × ¹¹⁵/₁₀₀ = $3565

⇒ P = ³⁵⁶⁵/_¹¹⁵/100

⇒ P = 3565 × ¹⁰⁰/₁₁₅

⇒ P = ^{3565 × 100}/₁₁₅

⇒ P = ³⁵⁶⁵⁰⁰/₁₁₅

⇒ P = $3100

Thus, the sum borrowed (P) = $3100 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 3565, then the Principal = ¹⁰⁰/₁₁₅ × 3565

= ^{100 × 3565}/₁₁₅

= ³⁵⁶⁵⁰⁰/₁₁₅

= 3100

Thus, Principal = $3100

Thus, the sum borrowed = $3100 Answer

Similar Questions

(1) What amount does Jennifer have to pay after 6 years if he takes a loan of $3250 at 10% simple interest?

(2) What amount does Joseph have to pay after 6 years if he takes a loan of $3700 at 10% simple interest?

(3) David took a loan of $4800 at the rate of 6% simple interest per annum. If he paid an amount of $6528 to clear the loan, then find the time period of the loan.

(4) Find the amount to be paid if Sarah borrowed a sum of $5850 at 5% simple interest for 7 years.

(5) Calculate the amount due after 10 years if Linda borrowed a sum of $5350 at a rate of 6% simple interest.

(6) What amount does Robert have to pay after 5 years if he takes a loan of $3100 at 10% simple interest?

(7) What amount will be due after 2 years if Andrew borrowed a sum of $3900 at a 10% simple interest?

(8) Calculate the amount due if Robert borrowed a sum of $3100 at 7% simple interest for 3 years.

(9) Calculate the amount due after 10 years if Linda borrowed a sum of $5350 at a rate of 10% simple interest.

(10) Calculate the amount due after 9 years if Richard borrowed a sum of $5600 at a rate of 9% simple interest.