Simple Interest
Math MCQs

Question :    Daniel had to pay $4715 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  $4100

Solution & Explanation

Solution

Given,

Amount (A) = $4715

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

$4715 = P (1 + 5% × 3)

⇒ $4715 = P (1 + ⁵/₁₀₀ × 3)

⇒ $4715 = P (1 + ^{5 × 3}/₁₀₀)

⇒ $4715 = P (1 + ¹⁵/₁₀₀)

⇒ $4715 = P (^{100 + 15}/₁₀₀)

⇒ $4715 = P × ¹¹⁵/₁₀₀

⇒ P × ¹¹⁵/₁₀₀ = $4715

⇒ P = ⁴⁷¹⁵/_¹¹⁵/100

⇒ P = 4715 × ¹⁰⁰/₁₁₅

⇒ P = ^{4715 × 100}/₁₁₅

⇒ P = ⁴⁷¹⁵⁰⁰/₁₁₅

⇒ P = $4100

Thus, the sum borrowed (P) = $4100 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 4715, then the Principal = ¹⁰⁰/₁₁₅ × 4715

= ^{100 × 4715}/₁₁₅

= ⁴⁷¹⁵⁰⁰/₁₁₅

= 4100

Thus, Principal = $4100

Thus, the sum borrowed = $4100 Answer

Similar Questions

(1) How much loan did Dorothy borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8700 to clear it?

(2) How much loan did Susan borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7062.5 to clear it?

(3) Calculate the amount due after 10 years if Linda borrowed a sum of $5350 at a rate of 4% simple interest.

(4) Find the amount to be paid if Barbara borrowed a sum of $5550 at 7% simple interest for 8 years.

(5) Calculate the amount due if John borrowed a sum of $3200 at 3% simple interest for 4 years.

(6) How much loan did Melissa borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8820 to clear it?

(7) Calculate the amount due after 10 years if Robert borrowed a sum of $5100 at a rate of 2% simple interest.

(8) What amount does Karen have to pay after 5 years if he takes a loan of $3950 at 7% simple interest?

(9) What amount will be due after 2 years if Donald borrowed a sum of $3750 at a 5% simple interest?

(10) Calculate the amount due after 9 years if Charles borrowed a sum of $5900 at a rate of 9% simple interest.