Simple Interest
Math MCQs

Question :    Jennifer took a loan of $4500 at the rate of 7% simple interest per annum. If he paid an amount of $7335 to clear the loan, then find the time period of the loan.

Correct Answer  9

Solution & Explanation

Solution

Given,

Principal (P) = $4500

Rate of Simple Interest (R) = 7% per annum

Amount (A) = $7335

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 = $7335 – $4500 = $2835

Thus, Simple Interest = $2835

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 × 2835}/_{4500 × 7}

= ²⁸³⁵⁰⁰/₃₁₅₀₀

= 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) = $4500

Rate of Simple Interest (R) = 7% per annum

Simple Interest = $2835 (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 = 7% of Principal

= 7% of $4500

= ⁷/₁₀₀ × 4500

= ^{7 × 4500}/₁₀₀

= ³¹⁵⁰⁰/₁₀₀ = 315

Thus, simple Interest for 1 year = $315

Now,

∵ If the simple Interest is $315, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₃₁₅ years

∴ If the simple Interest is $2835, then the time = ¹/₃₁₅ × 2835 years

= ^{1 × 2835}/₃₁₅ years

= ²⁸³⁵/₃₁₅ = 9 years

Thus, time (T) = 9 years Answer

Similar Questions

(1) What amount will be due after 2 years if Richard borrowed a sum of $3300 at a 10% simple interest?

(2) Charles took a loan of $5800 at the rate of 9% simple interest per annum. If he paid an amount of $11020 to clear the loan, then find the time period of the loan.

(3) Anthony had to pay $4816 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(4) Patricia took a loan of $4300 at the rate of 9% simple interest per annum. If he paid an amount of $8170 to clear the loan, then find the time period of the loan.

(5) Find the amount to be paid if David borrowed a sum of $5400 at 6% simple interest for 7 years.

(6) How much loan did David borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6480 to clear it?

(7) Michael had to pay $3795 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(8) Calculate the amount due if Richard borrowed a sum of $3600 at 6% simple interest for 3 years.

(9) Calculate the amount due after 9 years if Patricia borrowed a sum of $5150 at a rate of 5% simple interest.

(10) Nancy took a loan of $6300 at the rate of 10% simple interest per annum. If he paid an amount of $12600 to clear the loan, then find the time period of the loan.