Simple Interest
Math MCQs

Question :    William took a loan of $5000 at the rate of 7% simple interest per annum. If he paid an amount of $7800 to clear the loan, then find the time period of the loan.

Correct Answer  8

Solution & Explanation

Solution

Given,

Principal (P) = $5000

Rate of Simple Interest (R) = 7% per annum

Amount (A) = $7800

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 = $7800 – $5000 = $2800

Thus, Simple Interest = $2800

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 × 2800}/_{5000 × 7}

= ²⁸⁰⁰⁰⁰/₃₅₀₀₀

= 8 years (using formula)

Thus, Time (T) = 8 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) = $5000

Rate of Simple Interest (R) = 7% per annum

Simple Interest = $2800 (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 = 7% of Principal

= 7% of $5000

= ⁷/₁₀₀ × 5000

= ^{7 × 5000}/₁₀₀

= ³⁵⁰⁰⁰/₁₀₀ = 350

Thus, simple Interest for 1 year = $350

Now,

∵ If the simple Interest is $350, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₃₅₀ years

∴ If the simple Interest is $2800, then the time = ¹/₃₅₀ × 2800 years

= ^{1 × 2800}/₃₅₀ years

= ²⁸⁰⁰/₃₅₀ = 8 years

Thus, time (T) = 8 years Answer

Similar Questions

(1) Matthew took a loan of $6400 at the rate of 6% simple interest per annum. If he paid an amount of $10240 to clear the loan, then find the time period of the loan.

(2) Calculate the amount due if Robert borrowed a sum of $3100 at 4% simple interest for 3 years.

(3) In how much time a principal of $3050 will amount to $3507.5 at a simple interest of 5% per annum?

(4) Calculate the amount due if Jennifer borrowed a sum of $3250 at 2% simple interest for 4 years.

(5) Richard had to pay $4140 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(6) Calculate the amount due if Barbara borrowed a sum of $3550 at 10% simple interest for 4 years.

(7) Karen took a loan of $5900 at the rate of 8% simple interest per annum. If he paid an amount of $10620 to clear the loan, then find the time period of the loan.

(8) What amount does David have to pay after 5 years if he takes a loan of $3400 at 2% simple interest?

(9) Calculate the amount due if Linda borrowed a sum of $3350 at 10% simple interest for 4 years.

(10) Nancy took a loan of $6300 at the rate of 6% simple interest per annum. If he paid an amount of $9324 to clear the loan, then find the time period of the loan.