Simple Interest
Math MCQs

Question :    Elizabeth took a loan of $4900 at the rate of 6% simple interest per annum. If he paid an amount of $6664 to clear the loan, then find the time period of the loan.

Correct Answer  6

Solution & Explanation

Solution

Given,

Principal (P) = $4900

Rate of Simple Interest (R) = 6% per annum

Amount (A) = $6664

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 = $6664 – $4900 = $1764

Thus, Simple Interest = $1764

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 × 1764}/_{4900 × 6}

= ¹⁷⁶⁴⁰⁰/₂₉₄₀₀

= 6 years (using formula)

Thus, Time (T) = 6 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) = 6% per annum

Simple Interest = $1764 (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 = 6% of Principal

= 6% of $4900

= ⁶/₁₀₀ × 4900

= ^{6 × 4900}/₁₀₀

= ²⁹⁴⁰⁰/₁₀₀ = 294

Thus, simple Interest for 1 year = $294

Now,

∵ If the simple Interest is $294, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₂₉₄ years

∴ If the simple Interest is $1764, then the time = ¹/₂₉₄ × 1764 years

= ^{1 × 1764}/₂₉₄ years

= ¹⁷⁶⁴/₂₉₄ = 6 years

Thus, time (T) = 6 years Answer

Similar Questions

(1) Calculate the amount due after 10 years if Barbara borrowed a sum of $5550 at a rate of 4% simple interest.

(2) Calculate the amount due if Barbara borrowed a sum of $3550 at 4% simple interest for 4 years.

(3) Calculate the amount due after 9 years if Robert borrowed a sum of $5100 at a rate of 9% simple interest.

(4) Betty took a loan of $6500 at the rate of 10% simple interest per annum. If he paid an amount of $11700 to clear the loan, then find the time period of the loan.

(5) How much loan did Linda borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6420 to clear it?

(6) Calculate the amount due if Linda borrowed a sum of $3350 at 7% simple interest for 3 years.

(7) Find the amount to be paid if Charles borrowed a sum of $5900 at 10% simple interest for 8 years.

(8) Karen took a loan of $5900 at the rate of 9% simple interest per annum. If he paid an amount of $9617 to clear the loan, then find the time period of the loan.

(9) Find the amount to be paid if James borrowed a sum of $5000 at 5% simple interest for 8 years.

(10) If Kimberly paid $5022 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.