Simple Interest
Math MCQs

Question :    Jessica took a loan of $5500 at the rate of 9% simple interest per annum. If he paid an amount of $9460 to clear the loan, then find the time period of the loan.

Correct Answer  8

Solution & Explanation

Solution

Given,

Principal (P) = $5500

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

Amount (A) = $9460

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 = $9460 – $5500 = $3960

Thus, Simple Interest = $3960

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 × 3960}/_{5500 × 9}

= ³⁹⁶⁰⁰⁰/₄₉₅₀₀

= 8 years (using formula)

Thus, Time (T) = 8 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) = $5500

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

Simple Interest = $3960 (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 $5500

= ⁹/₁₀₀ × 5500

= ^{9 × 5500}/₁₀₀

= ⁴⁹⁵⁰⁰/₁₀₀ = 495

Thus, simple Interest for 1 year = $495

Now,

∵ If the simple Interest is $495, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₄₉₅ years

∴ If the simple Interest is $3960, then the time = ¹/₄₉₅ × 3960 years

= ^{1 × 3960}/₄₉₅ years

= ³⁹⁶⁰/₄₉₅ = 8 years

Thus, time (T) = 8 years Answer

Similar Questions

(1) William took a loan of $5000 at the rate of 9% simple interest per annum. If he paid an amount of $9500 to clear the loan, then find the time period of the loan.

(2) What amount does Michael have to pay after 6 years if he takes a loan of $3300 at 5% simple interest?

(3) Calculate the amount due if Christopher borrowed a sum of $4000 at 3% simple interest for 3 years.

(4) Calculate the amount due if Mary borrowed a sum of $3050 at 8% simple interest for 4 years.

(5) Calculate the amount due if William borrowed a sum of $3500 at 5% simple interest for 3 years.

(6) In how much time a principal of $3200 will amount to $3680 at a simple interest of 5% per annum?

(7) Find the amount to be paid if Patricia borrowed a sum of $5150 at 7% simple interest for 7 years.

(8) Patricia took a loan of $4300 at the rate of 6% simple interest per annum. If he paid an amount of $6622 to clear the loan, then find the time period of the loan.

(9) What amount does Barbara have to pay after 6 years if he takes a loan of $3550 at 10% simple interest?

(10) In how much time a principal of $3100 will amount to $3596 at a simple interest of 4% per annum?