Simple Interest
Math MCQs

Question :    Kimberly had to pay $4929 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  $4650

Solution & Explanation

Solution

Given,

Amount (A) = $4929

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

$4929 = P (1 + 2% × 3)

⇒ $4929 = P (1 + ²/₁₀₀ × 3)

⇒ $4929 = P (1 + ^{2 × 3}/₁₀₀)

⇒ $4929 = P (1 + ⁶/₁₀₀)

⇒ $4929 = P (^{100 + 6}/₁₀₀)

⇒ $4929 = P × ¹⁰⁶/₁₀₀

⇒ P × ¹⁰⁶/₁₀₀ = $4929

⇒ P = ⁴⁹²⁹/_¹⁰⁶/100

⇒ P = 4929 × ¹⁰⁰/₁₀₆

⇒ P = ^{4929 × 100}/₁₀₆

⇒ P = ⁴⁹²⁹⁰⁰/₁₀₆

⇒ P = $4650

Thus, the sum borrowed (P) = $4650 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 4929, then the Principal = ¹⁰⁰/₁₀₆ × 4929

= ^{100 × 4929}/₁₀₆

= ⁴⁹²⁹⁰⁰/₁₀₆

= 4650

Thus, Principal = $4650

Thus, the sum borrowed = $4650 Answer

Similar Questions

(1) Calculate the amount due after 9 years if Christopher borrowed a sum of $6000 at a rate of 3% simple interest.

(2) Find the amount to be paid if Karen borrowed a sum of $5950 at 6% simple interest for 7 years.

(3) Richard took a loan of $5200 at the rate of 6% simple interest per annum. If he paid an amount of $8008 to clear the loan, then find the time period of the loan.

(4) Calculate the amount due if Linda borrowed a sum of $3350 at 3% simple interest for 4 years.

(5) How much loan did Emily borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7425 to clear it?

(6) Donald took a loan of $7000 at the rate of 6% simple interest per annum. If he paid an amount of $9520 to clear the loan, then find the time period of the loan.

(7) Calculate the amount due if Mary borrowed a sum of $3050 at 2% simple interest for 3 years.

(8) Jessica had to pay $3975 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(9) What amount does Michael have to pay after 6 years if he takes a loan of $3300 at 7% simple interest?

(10) Calculate the amount due if Robert borrowed a sum of $3100 at 4% simple interest for 4 years.