Simple Interest
Math MCQs

Question :    Daniel had to pay $4592 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

Correct Answer  $4100

Solution & Explanation

Solution

Given,

Amount (A) = $4592

Rate of Simple Interest (R) = 4%

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

$4592 = P (1 + 4% × 3)

⇒ $4592 = P (1 + ⁴/₁₀₀ × 3)

⇒ $4592 = P (1 + ^{4 × 3}/₁₀₀)

⇒ $4592 = P (1 + ¹²/₁₀₀)

⇒ $4592 = P (^{100 + 12}/₁₀₀)

⇒ $4592 = P × ¹¹²/₁₀₀

⇒ P × ¹¹²/₁₀₀ = $4592

⇒ P = ⁴⁵⁹²/_¹¹²/100

⇒ P = 4592 × ¹⁰⁰/₁₁₂

⇒ P = ^{4592 × 100}/₁₁₂

⇒ P = ⁴⁵⁹²⁰⁰/₁₁₂

⇒ 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 = 4% per annum

Thus, Interest = 4% of principal

⇒ Interest = 4% of 100 = 4

Thus, Simple Interest for 1 year = 4

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 × 4 = 12

Thus, simple interest for 3 years = 12

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 12 = 112

Calculation of the Principal

Now,

∵ If the Amount is 112, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₁₂

∴ If the Amount is 4592, then the Principal = ¹⁰⁰/₁₁₂ × 4592

= ^{100 × 4592}/₁₁₂

= ⁴⁵⁹²⁰⁰/₁₁₂

= 4100

Thus, Principal = $4100

Thus, the sum borrowed = $4100 Answer

Similar Questions

(1) Find the amount to be paid if Barbara borrowed a sum of $5550 at 3% simple interest for 7 years.

(2) What amount does Thomas have to pay after 6 years if he takes a loan of $3800 at 6% simple interest?

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

(4) What amount does Richard have to pay after 5 years if he takes a loan of $3600 at 6% simple interest?

(5) 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?

(6) Lisa took a loan of $6100 at the rate of 7% simple interest per annum. If he paid an amount of $9943 to clear the loan, then find the time period of the loan.

(7) Find the amount to be paid if Linda borrowed a sum of $5350 at 2% simple interest for 8 years.

(8) Calculate the amount due after 9 years if Thomas borrowed a sum of $5800 at a rate of 10% simple interest.

(9) Michael had to pay $3597 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(10) If Charles paid $4368 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.