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) What amount does Sarah have to pay after 5 years if he takes a loan of $3850 at 3% simple interest?

(2) Anthony took a loan of $6600 at the rate of 6% simple interest per annum. If he paid an amount of $9768 to clear the loan, then find the time period of the loan.

(3) Find the amount to be paid if Christopher borrowed a sum of $6000 at 3% simple interest for 7 years.

(4) If Ashley paid $5460 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(5) What amount will be due after 2 years if Michael borrowed a sum of $3150 at a 10% simple interest?

(6) Matthew took a loan of $6400 at the rate of 7% simple interest per annum. If he paid an amount of $9088 to clear the loan, then find the time period of the loan.

(7) In how much time a principal of $3000 will amount to $3240 at a simple interest of 4% per annum?

(8) What amount does Patricia have to pay after 5 years if he takes a loan of $3150 at 2% simple interest?

(9) Karen took a loan of $5900 at the rate of 7% simple interest per annum. If he paid an amount of $8791 to clear the loan, then find the time period of the loan.

(10) Nancy took a loan of $6300 at the rate of 10% simple interest per annum. If he paid an amount of $11970 to clear the loan, then find the time period of the loan.