Simple Interest
Math MCQs

Question :    Daniel had to pay $4715 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  $4100

Solution & Explanation

Solution

Given,

Amount (A) = $4715

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

$4715 = P (1 + 5% × 3)

⇒ $4715 = P (1 + ⁵/₁₀₀ × 3)

⇒ $4715 = P (1 + ^{5 × 3}/₁₀₀)

⇒ $4715 = P (1 + ¹⁵/₁₀₀)

⇒ $4715 = P (^{100 + 15}/₁₀₀)

⇒ $4715 = P × ¹¹⁵/₁₀₀

⇒ P × ¹¹⁵/₁₀₀ = $4715

⇒ P = ⁴⁷¹⁵/_¹¹⁵/100

⇒ P = 4715 × ¹⁰⁰/₁₁₅

⇒ P = ^{4715 × 100}/₁₁₅

⇒ P = ⁴⁷¹⁵⁰⁰/₁₁₅

⇒ P = $4100

Thus, the sum borrowed (P) = $4100 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 4715, then the Principal = ¹⁰⁰/₁₁₅ × 4715

= ^{100 × 4715}/₁₁₅

= ⁴⁷¹⁵⁰⁰/₁₁₅

= 4100

Thus, Principal = $4100

Thus, the sum borrowed = $4100 Answer

Similar Questions

(1) Calculate the amount due after 9 years if Susan borrowed a sum of $5650 at a rate of 6% simple interest.

(2) Find the amount to be paid if Richard borrowed a sum of $5600 at 10% simple interest for 7 years.

(3) Calculate the amount due after 9 years if Jessica borrowed a sum of $5750 at a rate of 4% simple interest.

(4) What amount does Elizabeth have to pay after 6 years if he takes a loan of $3450 at 3% simple interest?

(5) Calculate the amount due if Mary borrowed a sum of $3050 at 10% simple interest for 3 years.

(6) What amount does Jennifer have to pay after 5 years if he takes a loan of $3250 at 7% simple interest?

(7) If Christopher paid $4480 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(8) Calculate the amount due if Christopher borrowed a sum of $4000 at 4% simple interest for 4 years.

(9) How much loan did Richard borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6440 to clear it?

(10) What amount will be due after 2 years if Mark borrowed a sum of $3700 at a 8% simple interest?