Simple Interest
Math MCQs

Question :    If Lisa paid $4860 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

Correct Answer  $4050

Solution & Explanation

Solution

Given,

Amount (A) = $4860

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

$4860 = P (1 + 5% × 4)

⇒ $4860 = P (1 + ⁵/₁₀₀ × 4)

⇒ $4860 = P (1 + ^{5 × 4}/₁₀₀)

⇒ $4860 = P (1 + ²⁰/₁₀₀)

⇒ $4860 = P (^{100 + 20}/₁₀₀)

⇒ $4860 = P × ¹²⁰/₁₀₀

⇒ P × ¹²⁰/₁₀₀ = $4860

⇒ P = ⁴⁸⁶⁰/_¹²⁰/100

⇒ P = 4860 × ¹⁰⁰/₁₂₀

⇒ P = ^{4860 × 100}/₁₂₀

⇒ P = ⁴⁸⁶⁰⁰⁰/₁₂₀

⇒ P = $4050

Thus, the sum borrowed (P) = $4050 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 4860, then the Principal = ¹⁰⁰/₁₂₀ × 4860

= ^{100 × 4860}/₁₂₀

= ⁴⁸⁶⁰⁰⁰/₁₂₀

= 4050

Thus, Principal = $4050

Thus, the sum borrowed = $4050 Answer

Similar Questions

(1) What amount will be due after 2 years if Steven borrowed a sum of $3800 at a 4% simple interest?

(2) Margaret took a loan of $6700 at the rate of 6% simple interest per annum. If he paid an amount of $9916 to clear the loan, then find the time period of the loan.

(3) Barbara took a loan of $5100 at the rate of 8% simple interest per annum. If he paid an amount of $8364 to clear the loan, then find the time period of the loan.

(4) If Kimberly paid $5580 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(5) Calculate the amount due after 9 years if Joseph borrowed a sum of $5700 at a rate of 3% simple interest.

(6) James took a loan of $4000 at the rate of 8% simple interest per annum. If he paid an amount of $6880 to clear the loan, then find the time period of the loan.

(7) Calculate the amount due after 9 years if Thomas borrowed a sum of $5800 at a rate of 2% simple interest.

(8) Find the amount to be paid if Richard borrowed a sum of $5600 at 8% simple interest for 7 years.

(9) James had to pay $3360 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(10) What amount does Christopher have to pay after 6 years if he takes a loan of $4000 at 2% simple interest?