Simple Interest
Math MCQs

Question :    If Betty paid $4590 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

Correct Answer  $4250

Solution & Explanation

Solution

Given,

Amount (A) = $4590

Rate of Simple Interest (R) = 2%

Time (T) = 4 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

$4590 = P (1 + 2% × 4)

⇒ $4590 = P (1 + ²/₁₀₀ × 4)

⇒ $4590 = P (1 + ^{2 × 4}/₁₀₀)

⇒ $4590 = P (1 + ⁸/₁₀₀)

⇒ $4590 = P (^{100 + 8}/₁₀₀)

⇒ $4590 = P × ¹⁰⁸/₁₀₀

⇒ P × ¹⁰⁸/₁₀₀ = $4590

⇒ P = ⁴⁵⁹⁰/_¹⁰⁸/100

⇒ P = 4590 × ¹⁰⁰/₁₀₈

⇒ P = ^{4590 × 100}/₁₀₈

⇒ P = ⁴⁵⁹⁰⁰⁰/₁₀₈

⇒ P = $4250

Thus, the sum borrowed (P) = $4250 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 = 4 years

So, we need to calculate the simple interest for the given time period, which is 4 years

Thus, Simple Interest for 4 years = 4 × Simple Interest for 1 year

= 4 × 2 = 8

Thus, simple interest for 4 years = 8

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 8 = 108

Calculation of the Principal

Now,

∵ If the Amount is 108, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₀₈

∴ If the Amount is 4590, then the Principal = ¹⁰⁰/₁₀₈ × 4590

= ^{100 × 4590}/₁₀₈

= ⁴⁵⁹⁰⁰⁰/₁₀₈

= 4250

Thus, Principal = $4250

Thus, the sum borrowed = $4250 Answer

Similar Questions

(1) Find the amount to be paid if Sarah borrowed a sum of $5850 at 10% simple interest for 7 years.

(2) Linda took a loan of $4700 at the rate of 9% simple interest per annum. If he paid an amount of $7238 to clear the loan, then find the time period of the loan.

(3) How much loan did Carol borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8107.5 to clear it?

(4) Jessica took a loan of $5500 at the rate of 8% simple interest per annum. If he paid an amount of $9020 to clear the loan, then find the time period of the loan.

(5) Calculate the amount due after 9 years if James borrowed a sum of $5000 at a rate of 6% simple interest.

(6) Find the amount to be paid if Susan borrowed a sum of $5650 at 10% simple interest for 7 years.

(7) What amount does Jessica have to pay after 6 years if he takes a loan of $3750 at 7% simple interest?

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

(9) If Patricia borrowed $3150 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.

(10) Christopher took a loan of $6000 at the rate of 7% simple interest per annum. If he paid an amount of $10200 to clear the loan, then find the time period of the loan.