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 $7240 to clear the loan, then find the time period of the loan.

Correct Answer  9

Solution & Explanation

Solution

Given,

Principal (P) = $4000

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

Amount (A) = $7240

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 = $7240 – $4000 = $3240

Thus, Simple Interest = $3240

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 × 3240}/_{4000 × 9}

= ³²⁴⁰⁰⁰/₃₆₀₀₀

= 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) = $4000

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

Simple Interest = $3240 (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 $3240, then the time = ¹/₃₆₀ × 3240 years

= ^{1 × 3240}/₃₆₀ years

= ³²⁴⁰/₃₆₀ = 9 years

Thus, time (T) = 9 years Answer

Similar Questions

(1) Jessica took a loan of $5500 at the rate of 6% simple interest per annum. If he paid an amount of $8800 to clear the loan, then find the time period of the loan.

(2) What amount will be due after 2 years if Andrew borrowed a sum of $3900 at a 9% simple interest?

(3) What amount does John have to pay after 5 years if he takes a loan of $3200 at 5% simple interest?

(4) Calculate the amount due after 9 years if Karen borrowed a sum of $5950 at a rate of 5% simple interest.

(5) Richard took a loan of $5200 at the rate of 10% simple interest per annum. If he paid an amount of $10400 to clear the loan, then find the time period of the loan.

(6) Calculate the amount due if Linda borrowed a sum of $3350 at 9% simple interest for 3 years.

(7) John took a loan of $4400 at the rate of 6% simple interest per annum. If he paid an amount of $7040 to clear the loan, then find the time period of the loan.

(8) Michael took a loan of $4600 at the rate of 8% simple interest per annum. If he paid an amount of $7912 to clear the loan, then find the time period of the loan.

(9) What amount does Charles have to pay after 6 years if he takes a loan of $3900 at 4% simple interest?

(10) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 8% simple interest?