Simple Interest
Math MCQs

Question :    Thomas had to pay $4028 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

Correct Answer  $3800

Solution & Explanation

Solution

Given,

Amount (A) = $4028

Rate of Simple Interest (R) = 2%

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

$4028 = P (1 + 2% × 3)

⇒ $4028 = P (1 + ²/₁₀₀ × 3)

⇒ $4028 = P (1 + ^{2 × 3}/₁₀₀)

⇒ $4028 = P (1 + ⁶/₁₀₀)

⇒ $4028 = P (^{100 + 6}/₁₀₀)

⇒ $4028 = P × ¹⁰⁶/₁₀₀

⇒ P × ¹⁰⁶/₁₀₀ = $4028

⇒ P = ⁴⁰²⁸/_¹⁰⁶/100

⇒ P = 4028 × ¹⁰⁰/₁₀₆

⇒ P = ^{4028 × 100}/₁₀₆

⇒ P = ⁴⁰²⁸⁰⁰/₁₀₆

⇒ P = $3800

Thus, the sum borrowed (P) = $3800 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 = 2% per annum

Thus, Interest = 2% of principal

⇒ Interest = 2% of 100 = 2

Thus, Simple Interest for 1 year = 2

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 × 2 = 6

Thus, simple interest for 3 years = 6

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 6 = 106

Calculation of the Principal

Now,

∵ If the Amount is 106, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₀₆

∴ If the Amount is 4028, then the Principal = ¹⁰⁰/₁₀₆ × 4028

= ^{100 × 4028}/₁₀₆

= ⁴⁰²⁸⁰⁰/₁₀₆

= 3800

Thus, Principal = $3800

Thus, the sum borrowed = $3800 Answer

Similar Questions

(1) Calculate the amount due if Thomas borrowed a sum of $3800 at 7% simple interest for 4 years.

(2) What amount does Mary have to pay after 5 years if he takes a loan of $3050 at 8% simple interest?

(3) What amount does John have to pay after 6 years if he takes a loan of $3200 at 6% simple interest?

(4) What amount does Michael have to pay after 5 years if he takes a loan of $3300 at 6% simple interest?

(5) Daniel took a loan of $6200 at the rate of 7% simple interest per annum. If he paid an amount of $9672 to clear the loan, then find the time period of the loan.

(6) Joshua had to pay $5488 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(7) Find the amount to be paid if Christopher borrowed a sum of $6000 at 2% simple interest for 8 years.

(8) What amount does John have to pay after 6 years if he takes a loan of $3200 at 5% simple interest?

(9) What amount does Charles have to pay after 5 years if he takes a loan of $3900 at 8% simple interest?

(10) How much loan did Nancy borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7072.5 to clear it?