Simple Interest
Math MCQs

Question :    If Jennifer paid $3510 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

Correct Answer  $3250

Solution & Explanation

Solution

Given,

Amount (A) = $3510

Rate of Simple Interest (R) = 2%

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

$3510 = P (1 + 2% × 4)

⇒ $3510 = P (1 + ²/₁₀₀ × 4)

⇒ $3510 = P (1 + ^{2 × 4}/₁₀₀)

⇒ $3510 = P (1 + ⁸/₁₀₀)

⇒ $3510 = P (^{100 + 8}/₁₀₀)

⇒ $3510 = P × ¹⁰⁸/₁₀₀

⇒ P × ¹⁰⁸/₁₀₀ = $3510

⇒ P = ³⁵¹⁰/_¹⁰⁸/100

⇒ P = 3510 × ¹⁰⁰/₁₀₈

⇒ P = ^{3510 × 100}/₁₀₈

⇒ P = ³⁵¹⁰⁰⁰/₁₀₈

⇒ P = $3250

Thus, the sum borrowed (P) = $3250 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 = 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 × 2 = 8

Thus, simple interest for 4 years = 8

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 8 = 108

Calculation of the Principal

Now,

∵ If the Amount is 108, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₀₈

∴ If the Amount is 3510, then the Principal = ¹⁰⁰/₁₀₈ × 3510

= ^{100 × 3510}/₁₀₈

= ³⁵¹⁰⁰⁰/₁₀₈

= 3250

Thus, Principal = $3250

Thus, the sum borrowed = $3250 Answer

Similar Questions

(1) What amount does Elizabeth have to pay after 6 years if he takes a loan of $3450 at 2% simple interest?

(2) What amount will be due after 2 years if William borrowed a sum of $3250 at a 4% simple interest?

(3) How much loan did Sandra borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7095 to clear it?

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

(5) If Margaret paid $4698 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(6) What amount does Jessica have to pay after 6 years if he takes a loan of $3750 at 5% simple interest?

(7) Find the amount to be paid if Robert borrowed a sum of $5100 at 8% simple interest for 7 years.

(8) What amount does Jennifer have to pay after 6 years if he takes a loan of $3250 at 8% simple interest?

(9) In how much time a principal of $3200 will amount to $3456 at a simple interest of 2% per annum?

(10) What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 6% simple interest?