Simple Interest
Math MCQs

Question :    If Betty paid $5100 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

Correct Answer  $4250

Solution & Explanation

Solution

Given,

Amount (A) = $5100

Rate of Simple Interest (R) = 5%

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

$5100 = P (1 + 5% × 4)

⇒ $5100 = P (1 + ⁵/₁₀₀ × 4)

⇒ $5100 = P (1 + ^{5 × 4}/₁₀₀)

⇒ $5100 = P (1 + ²⁰/₁₀₀)

⇒ $5100 = P (^{100 + 20}/₁₀₀)

⇒ $5100 = P × ¹²⁰/₁₀₀

⇒ P × ¹²⁰/₁₀₀ = $5100

⇒ P = ⁵¹⁰⁰/_¹²⁰/100

⇒ P = 5100 × ¹⁰⁰/₁₂₀

⇒ P = ^{5100 × 100}/₁₂₀

⇒ P = ⁵¹⁰⁰⁰⁰/₁₂₀

⇒ 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 = 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 = 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 × 5 = 20

Thus, simple interest for 4 years = 20

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 20 = 120

Calculation of the Principal

Now,

∵ If the Amount is 120, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₂₀

∴ If the Amount is 5100, then the Principal = ¹⁰⁰/₁₂₀ × 5100

= ^{100 × 5100}/₁₂₀

= ⁵¹⁰⁰⁰⁰/₁₂₀

= 4250

Thus, Principal = $4250

Thus, the sum borrowed = $4250 Answer

Similar Questions

(1) Mary had to pay $3416 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(2) What amount does Mary have to pay after 6 years if he takes a loan of $3050 at 5% simple interest?

(3) How much loan did Nancy borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7380 to clear it?

(4) How much loan did Kenneth borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7700 to clear it?

(5) What amount will be due after 2 years if Mark borrowed a sum of $3700 at a 6% simple interest?

(6) Linda took a loan of $4700 at the rate of 8% simple interest per annum. If he paid an amount of $8460 to clear the loan, then find the time period of the loan.

(7) What amount does Robert have to pay after 5 years if he takes a loan of $3100 at 8% simple interest?

(8) Christopher took a loan of $6000 at the rate of 9% simple interest per annum. If he paid an amount of $10320 to clear the loan, then find the time period of the loan.

(9) What amount does Karen have to pay after 5 years if he takes a loan of $3950 at 9% simple interest?

(10) Find the amount to be paid if Thomas borrowed a sum of $5800 at 2% simple interest for 7 years.