Simple Interest
Math MCQs

Question :    Nancy took a loan of $6300 at the rate of 9% simple interest per annum. If he paid an amount of $11970 to clear the loan, then find the time period of the loan.

Correct Answer  10

Solution & Explanation

Solution

Given,

Principal (P) = $6300

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

Amount (A) = $11970

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 = $11970 – $6300 = $5670

Thus, Simple Interest = $5670

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 × 5670}/_{6300 × 9}

= ⁵⁶⁷⁰⁰⁰/₅₆₇₀₀

= 10 years (using formula)

Thus, Time (T) = 10 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) = $6300

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

Simple Interest = $5670 (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 $6300

= ⁹/₁₀₀ × 6300

= ^{9 × 6300}/₁₀₀

= ⁵⁶⁷⁰⁰/₁₀₀ = 567

Thus, simple Interest for 1 year = $567

Now,

∵ If the simple Interest is $567, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₅₆₇ years

∴ If the simple Interest is $5670, then the time = ¹/₅₆₇ × 5670 years

= ^{1 × 5670}/₅₆₇ years

= ⁵⁶⁷⁰/₅₆₇ = 10 years

Thus, time (T) = 10 years Answer

Similar Questions

(1) Calculate the amount due after 9 years if Robert borrowed a sum of $5100 at a rate of 2% simple interest.

(2) How much loan did George borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8030 to clear it?

(3) What amount does Karen have to pay after 6 years if he takes a loan of $3950 at 8% simple interest?

(4) Calculate the amount due after 9 years if Michael borrowed a sum of $5300 at a rate of 2% simple interest.

(5) Calculate the amount due after 9 years if Elizabeth borrowed a sum of $5450 at a rate of 8% simple interest.

(6) Calculate the amount due if Barbara borrowed a sum of $3550 at 10% simple interest for 3 years.

(7) How much loan did Joseph borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6270 to clear it?

(8) Find the amount to be paid if Thomas borrowed a sum of $5800 at 4% simple interest for 7 years.

(9) Calculate the amount due after 10 years if Christopher borrowed a sum of $6000 at a rate of 2% simple interest.

(10) Elizabeth took a loan of $4900 at the rate of 10% simple interest per annum. If he paid an amount of $8330 to clear the loan, then find the time period of the loan.