Simple Interest
Math MCQs

Question :    James took a loan of $4000 at the rate of 9% simple interest per annum. If he paid an amount of $6160 to clear the loan, then find the time period of the loan.

Correct Answer  6

Solution & Explanation

Solution

Given,

Principal (P) = $4000

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

Amount (A) = $6160

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 = $6160 – $4000 = $2160

Thus, Simple Interest = $2160

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 × 2160}/_{4000 × 9}

= ²¹⁶⁰⁰⁰/₃₆₀₀₀

= 6 years (using formula)

Thus, Time (T) = 6 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) = $4000

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

Simple Interest = $2160 (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 $4000

= ⁹/₁₀₀ × 4000

= ^{9 × 4000}/₁₀₀

= ³⁶⁰⁰⁰/₁₀₀ = 360

Thus, simple Interest for 1 year = $360

Now,

∵ If the simple Interest is $360, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₃₆₀ years

∴ If the simple Interest is $2160, then the time = ¹/₃₆₀ × 2160 years

= ^{1 × 2160}/₃₆₀ years

= ²¹⁶⁰/₃₆₀ = 6 years

Thus, time (T) = 6 years Answer

Similar Questions

(1) Find the amount to be paid if Patricia borrowed a sum of $5150 at 4% simple interest for 8 years.

(2) Find the amount to be paid if Richard borrowed a sum of $5600 at 10% simple interest for 7 years.

(3) Find the amount to be paid if Patricia borrowed a sum of $5150 at 10% simple interest for 8 years.

(4) Calculate the amount due if Susan borrowed a sum of $3650 at 9% simple interest for 4 years.

(5) How much loan did James borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6000 to clear it?

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

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

(8) Calculate the amount due after 10 years if Christopher borrowed a sum of $6000 at a rate of 3% simple interest.

(9) Calculate the amount due if David borrowed a sum of $3400 at 7% simple interest for 4 years.

(10) Sarah took a loan of $5700 at the rate of 9% simple interest per annum. If he paid an amount of $9804 to clear the loan, then find the time period of the loan.