Simple Interest
Math MCQs

Question :    Donna had to pay $5141 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  $4850

Solution & Explanation

Solution

Given,

Amount (A) = $5141

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

$5141 = P (1 + 2% × 3)

⇒ $5141 = P (1 + ²/₁₀₀ × 3)

⇒ $5141 = P (1 + ^{2 × 3}/₁₀₀)

⇒ $5141 = P (1 + ⁶/₁₀₀)

⇒ $5141 = P (^{100 + 6}/₁₀₀)

⇒ $5141 = P × ¹⁰⁶/₁₀₀

⇒ P × ¹⁰⁶/₁₀₀ = $5141

⇒ P = ⁵¹⁴¹/_¹⁰⁶/100

⇒ P = 5141 × ¹⁰⁰/₁₀₆

⇒ P = ^{5141 × 100}/₁₀₆

⇒ P = ⁵¹⁴¹⁰⁰/₁₀₆

⇒ P = $4850

Thus, the sum borrowed (P) = $4850 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 5141, then the Principal = ¹⁰⁰/₁₀₆ × 5141

= ^{100 × 5141}/₁₀₆

= ⁵¹⁴¹⁰⁰/₁₀₆

= 4850

Thus, Principal = $4850

Thus, the sum borrowed = $4850 Answer

Similar Questions

(1) In how much time a principal of $3000 will amount to $3360 at a simple interest of 4% per annum?

(2) What amount does Patricia have to pay after 6 years if he takes a loan of $3150 at 2% simple interest?

(3) In how much time a principal of $3050 will amount to $3172 at a simple interest of 2% per annum?

(4) What amount does Barbara have to pay after 5 years if he takes a loan of $3550 at 10% simple interest?

(5) Calculate the amount due if Jennifer borrowed a sum of $3250 at 10% simple interest for 3 years.

(6) William took a loan of $5000 at the rate of 10% simple interest per annum. If he paid an amount of $8000 to clear the loan, then find the time period of the loan.

(7) What amount does Elizabeth have to pay after 5 years if he takes a loan of $3450 at 5% simple interest?

(8) How much loan did Sandra borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7417.5 to clear it?

(9) What amount will be due after 2 years if Steven borrowed a sum of $3800 at a 10% simple interest?

(10) Nancy took a loan of $6300 at the rate of 8% simple interest per annum. If he paid an amount of $9828 to clear the loan, then find the time period of the loan.