Simple Interest
Math MCQs

Question :    John took a loan of $4400 at the rate of 8% simple interest per annum. If he paid an amount of $7216 to clear the loan, then find the time period of the loan.

Correct Answer  8

Solution & Explanation

Solution

Given,

Principal (P) = $4400

Rate of Simple Interest (R) = 8% per annum

Amount (A) = $7216

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 = $7216 – $4400 = $2816

Thus, Simple Interest = $2816

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 × 2816}/_{4400 × 8}

= ²⁸¹⁶⁰⁰/₃₅₂₀₀

= 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) = $4400

Rate of Simple Interest (R) = 8% per annum

Simple Interest = $2816 (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 = 8% of Principal

= 8% of $4400

= ⁸/₁₀₀ × 4400

= ^{8 × 4400}/₁₀₀

= ³⁵²⁰⁰/₁₀₀ = 352

Thus, simple Interest for 1 year = $352

Now,

∵ If the simple Interest is $352, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₃₅₂ years

∴ If the simple Interest is $2816, then the time = ¹/₃₅₂ × 2816 years

= ^{1 × 2816}/₃₅₂ years

= ²⁸¹⁶/₃₅₂ = 8 years

Thus, time (T) = 8 years Answer

Similar Questions

(1) What amount does Jennifer have to pay after 5 years if he takes a loan of $3250 at 6% simple interest?

(2) James took a loan of $4000 at the rate of 7% simple interest per annum. If he paid an amount of $6240 to clear the loan, then find the time period of the loan.

(3) Find the amount to be paid if Susan borrowed a sum of $5650 at 7% simple interest for 8 years.

(4) Calculate the amount due if Joseph borrowed a sum of $3700 at 9% simple interest for 4 years.

(5) What amount will be due after 2 years if Andrew borrowed a sum of $3900 at a 6% simple interest?

(6) Calculate the amount due after 9 years if Charles borrowed a sum of $5900 at a rate of 6% simple interest.

(7) Calculate the amount due after 9 years if James borrowed a sum of $5000 at a rate of 2% simple interest.

(8) Calculate the amount due after 10 years if David borrowed a sum of $5400 at a rate of 8% simple interest.

(9) Calculate the amount due if Mary borrowed a sum of $3050 at 5% simple interest for 4 years.

(10) James had to pay $3450 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.