Simple Interest
Math MCQs

Question :    Elizabeth had to pay $3967.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

Correct Answer  $3450

Solution & Explanation

Solution

Given,

Amount (A) = $3967.5

Rate of Simple Interest (R) = 5%

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

$3967.5 = P (1 + 5% × 3)

⇒ $3967.5 = P (1 + ⁵/₁₀₀ × 3)

⇒ $3967.5 = P (1 + ^{5 × 3}/₁₀₀)

⇒ $3967.5 = P (1 + ¹⁵/₁₀₀)

⇒ $3967.5 = P (^{100 + 15}/₁₀₀)

⇒ $3967.5 = P × ¹¹⁵/₁₀₀

⇒ P × ¹¹⁵/₁₀₀ = $3967.5

⇒ P = ^3967.5/_¹¹⁵/100

⇒ P = 3967.5 × ¹⁰⁰/₁₁₅

⇒ P = ^{3967.5 × 100}/₁₁₅

⇒ P = ³⁹⁶⁷⁵⁰/₁₁₅

⇒ P = $3450

Thus, the sum borrowed (P) = $3450 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 = 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 × 5 = 15

Thus, simple interest for 3 years = 15

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 15 = 115

Calculation of the Principal

Now,

∵ If the Amount is 115, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₁₅

∴ If the Amount is 3967.5, then the Principal = ¹⁰⁰/₁₁₅ × 3967.5

= ^{100 × 3967.5}/₁₁₅

= ³⁹⁶⁷⁵⁰/₁₁₅

= 3450

Thus, Principal = $3450

Thus, the sum borrowed = $3450 Answer

Similar Questions

(1) If John paid $3584 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(2) Calculate the amount due after 9 years if Barbara borrowed a sum of $5550 at a rate of 6% simple interest.

(3) Kimberly had to pay $5208 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(4) What amount does Linda have to pay after 6 years if he takes a loan of $3350 at 4% simple interest?

(5) In how much time a principal of $3200 will amount to $3840 at a simple interest of 4% per annum?

(6) What amount does Karen have to pay after 6 years if he takes a loan of $3950 at 8% simple interest?

(7) How much loan did Michael borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6625 to clear it?

(8) Find the amount to be paid if Sarah borrowed a sum of $5850 at 3% simple interest for 7 years.

(9) David took a loan of $4800 at the rate of 8% simple interest per annum. If he paid an amount of $7104 to clear the loan, then find the time period of the loan.

(10) Jessica took a loan of $5500 at the rate of 8% simple interest per annum. If he paid an amount of $9900 to clear the loan, then find the time period of the loan.