Simple Interest
Math MCQs

Question :    Susan had to pay $4088 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  $3650

Solution & Explanation

Solution

Given,

Amount (A) = $4088

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

$4088 = P (1 + 4% × 3)

⇒ $4088 = P (1 + ⁴/₁₀₀ × 3)

⇒ $4088 = P (1 + ^{4 × 3}/₁₀₀)

⇒ $4088 = P (1 + ¹²/₁₀₀)

⇒ $4088 = P (^{100 + 12}/₁₀₀)

⇒ $4088 = P × ¹¹²/₁₀₀

⇒ P × ¹¹²/₁₀₀ = $4088

⇒ P = ⁴⁰⁸⁸/_¹¹²/100

⇒ P = 4088 × ¹⁰⁰/₁₁₂

⇒ P = ^{4088 × 100}/₁₁₂

⇒ P = ⁴⁰⁸⁸⁰⁰/₁₁₂

⇒ P = $3650

Thus, the sum borrowed (P) = $3650 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 4088, then the Principal = ¹⁰⁰/₁₁₂ × 4088

= ^{100 × 4088}/₁₁₂

= ⁴⁰⁸⁸⁰⁰/₁₁₂

= 3650

Thus, Principal = $3650

Thus, the sum borrowed = $3650 Answer

Similar Questions

(1) Calculate the amount due after 9 years if Patricia borrowed a sum of $5150 at a rate of 9% simple interest.

(2) What amount does Jennifer have to pay after 5 years if he takes a loan of $3250 at 7% simple interest?

(3) Mary took a loan of $4100 at the rate of 10% simple interest per annum. If he paid an amount of $6560 to clear the loan, then find the time period of the loan.

(4) How much loan did Joseph borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6840 to clear it?

(5) Donald took a loan of $7000 at the rate of 8% simple interest per annum. If he paid an amount of $12600 to clear the loan, then find the time period of the loan.

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

(7) Calculate the amount due after 9 years if Christopher borrowed a sum of $6000 at a rate of 4% simple interest.

(8) What amount does David have to pay after 6 years if he takes a loan of $3400 at 9% simple interest?

(9) What amount does Elizabeth have to pay after 5 years if he takes a loan of $3450 at 8% simple interest?

(10) What amount does Barbara have to pay after 6 years if he takes a loan of $3550 at 2% simple interest?