Simple Interest
Math MCQs

Question :    Karen took a loan of $5900 at the rate of 9% simple interest per annum. If he paid an amount of $11210 to clear the loan, then find the time period of the loan.

Correct Answer  10

Solution & Explanation

Solution

Given,

Principal (P) = $5900

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

Amount (A) = $11210

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 = $11210 – $5900 = $5310

Thus, Simple Interest = $5310

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 × 5310}/_{5900 × 9}

= ⁵³¹⁰⁰⁰/₅₃₁₀₀

= 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) = $5900

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

Simple Interest = $5310 (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 $5900

= ⁹/₁₀₀ × 5900

= ^{9 × 5900}/₁₀₀

= ⁵³¹⁰⁰/₁₀₀ = 531

Thus, simple Interest for 1 year = $531

Now,

∵ If the simple Interest is $531, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₅₃₁ years

∴ If the simple Interest is $5310, then the time = ¹/₅₃₁ × 5310 years

= ^{1 × 5310}/₅₃₁ years

= ⁵³¹⁰/₅₃₁ = 10 years

Thus, time (T) = 10 years Answer

Similar Questions

(1) Calculate the amount due after 10 years if Sarah borrowed a sum of $5850 at a rate of 3% simple interest.

(2) Calculate the amount due after 9 years if Richard borrowed a sum of $5600 at a rate of 4% simple interest.

(3) How much loan did Sharon borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8912.5 to clear it?

(4) Susan took a loan of $5300 at the rate of 8% simple interest per annum. If he paid an amount of $8692 to clear the loan, then find the time period of the loan.

(5) David took a loan of $4800 at the rate of 9% simple interest per annum. If he paid an amount of $8256 to clear the loan, then find the time period of the loan.

(6) Find the amount to be paid if James borrowed a sum of $5000 at 9% simple interest for 7 years.

(7) What amount does Michael have to pay after 5 years if he takes a loan of $3300 at 10% simple interest?

(8) James took a loan of $4000 at the rate of 8% simple interest per annum. If he paid an amount of $6880 to clear the loan, then find the time period of the loan.

(9) What amount does William have to pay after 5 years if he takes a loan of $3500 at 9% simple interest?

(10) Calculate the amount due after 9 years if Barbara borrowed a sum of $5550 at a rate of 7% simple interest.