Simple Interest
Math MCQs

Question :    Elizabeth took a loan of $4900 at the rate of 9% simple interest per annum. If he paid an amount of $8869 to clear the loan, then find the time period of the loan.

Correct Answer  9

Solution & Explanation

Solution

Given,

Principal (P) = $4900

Rate of Simple Interest (R) = 9% per annum

Amount (A) = $8869

Thus, time (T) = ?

Method (1) Using Formula

Calculation of Simple Interest, when Principal and Amount are given

Formual to Calculate Simple Interest when Principal and Amount are given

We know that, Amount (A) = Principal (P) + Simple Interest (SI)

⇒ Simple Interest (SI) = Amount – Principal

⇒ SI = $8869 – $4900 = $3969

Thus, Simple Interest = $3969

Calculation of the Time using forumula when Amount, Simple Interest and Principal are known

Formula to find the Time (T)

Time (T) = ^{100 × Simple Interest}/_{Principal × Rate of Interest}

⇒ T = ^{100 × SI}/_{P × R}

Thus, Time (T) = ^{100 × 3969}/_{4900 × 9}

= ³⁹⁶⁹⁰⁰/₄₄₁₀₀

= 9 years (using formula)

Thus, Time (T) = 9 years (from time taken before calculation)Answer

Calculation of the Time using Unitary Method when Amount, Simple Interest and Principal are known

Here, we have

Principal (P) = $4900

Rate of Simple Interest (R) = 9% per annum

Simple Interest = $3969 (As calculated above by subtracting Principal from the Amount given)

We know that, interest is calculated on the basis of the Principal.

This means Simple Interest for 1 year = Rate of simple interest × Principal

Thus, Simple Interest for 1 year = 9% of Principal

= 9% of $4900

= ⁹/₁₀₀ × 4900

= ^{9 × 4900}/₁₀₀

= ⁴⁴¹⁰⁰/₁₀₀ = 441

Thus, simple Interest for 1 year = $441

Now,

∵ If the simple Interest is $441, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₄₄₁ years

∴ If the simple Interest is $3969, then the time = ¹/₄₄₁ × 3969 years

= ^{1 × 3969}/₄₄₁ years

= ³⁹⁶⁹/₄₄₁ = 9 years

Thus, time (T) = 9 years Answer

Similar Questions

(1) Lisa had to pay $4293 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(2) Find the amount to be paid if David borrowed a sum of $5400 at 2% simple interest for 8 years.

(3) How much loan did Lisa borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6957.5 to clear it?

(4) Find the amount to be paid if Robert borrowed a sum of $5100 at 9% simple interest for 8 years.

(5) What amount does Robert have to pay after 5 years if he takes a loan of $3100 at 5% simple interest?

(6) Find the amount to be paid if Thomas borrowed a sum of $5800 at 2% simple interest for 7 years.

(7) James had to pay $3270 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(8) Joseph took a loan of $5400 at the rate of 9% simple interest per annum. If he paid an amount of $8802 to clear the loan, then find the time period of the loan.

(9) Calculate the amount due if Richard borrowed a sum of $3600 at 8% simple interest for 3 years.

(10) How much loan did Jessica borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6900 to clear it?