Simple Interest
Math MCQs

Question :    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.

Correct Answer  9

Solution & Explanation

Solution

Given,

Principal (P) = $4300

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

Amount (A) = $6622

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 = $6622 – $4300 = $2322

Thus, Simple Interest = $2322

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 × 2322}/_{4300 × 6}

= ²³²²⁰⁰/₂₅₈₀₀

= 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) = $4300

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

Simple Interest = $2322 (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 $4300

= ⁶/₁₀₀ × 4300

= ^{6 × 4300}/₁₀₀

= ²⁵⁸⁰⁰/₁₀₀ = 258

Thus, simple Interest for 1 year = $258

Now,

∵ If the simple Interest is $258, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₂₅₈ years

∴ If the simple Interest is $2322, then the time = ¹/₂₅₈ × 2322 years

= ^{1 × 2322}/₂₅₈ years

= ²³²²/₂₅₈ = 9 years

Thus, time (T) = 9 years Answer

Similar Questions

(1) Susan had to pay $4088 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(2) Calculate the amount due if Patricia borrowed a sum of $3150 at 7% simple interest for 3 years.

(3) What amount does James have to pay after 6 years if he takes a loan of $3000 at 10% simple interest?

(4) Joseph took a loan of $5400 at the rate of 10% simple interest per annum. If he paid an amount of $9180 to clear the loan, then find the time period of the loan.

(5) Ashley had to pay $4823 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(6) Joseph took a loan of $5400 at the rate of 9% simple interest per annum. If he paid an amount of $9774 to clear the loan, then find the time period of the loan.

(7) How much loan did Rebecca borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9562.5 to clear it?

(8) Linda took a loan of $4700 at the rate of 9% simple interest per annum. If he paid an amount of $8930 to clear the loan, then find the time period of the loan.

(9) Calculate the amount due if Jessica borrowed a sum of $3750 at 4% simple interest for 3 years.

(10) Robert took a loan of $4200 at the rate of 6% simple interest per annum. If he paid an amount of $6468 to clear the loan, then find the time period of the loan.