Simple Interest
Math MCQs

Question :    Margaret took a loan of $6700 at the rate of 8% simple interest per annum. If he paid an amount of $10988 to clear the loan, then find the time period of the loan.

Correct Answer  8

Solution & Explanation

Solution

Given,

Principal (P) = $6700

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

Amount (A) = $10988

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 = $10988 – $6700 = $4288

Thus, Simple Interest = $4288

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 × 4288}/_{6700 × 8}

= ⁴²⁸⁸⁰⁰/₅₃₆₀₀

= 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) = $6700

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

Simple Interest = $4288 (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 $6700

= ⁸/₁₀₀ × 6700

= ^{8 × 6700}/₁₀₀

= ⁵³⁶⁰⁰/₁₀₀ = 536

Thus, simple Interest for 1 year = $536

Now,

∵ If the simple Interest is $536, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₅₃₆ years

∴ If the simple Interest is $4288, then the time = ¹/₅₃₆ × 4288 years

= ^{1 × 4288}/₅₃₆ years

= ⁴²⁸⁸/₅₃₆ = 8 years

Thus, time (T) = 8 years Answer

Similar Questions

(1) Anthony took a loan of $6600 at the rate of 10% simple interest per annum. If he paid an amount of $11220 to clear the loan, then find the time period of the loan.

(2) If William borrowed $3500 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.

(3) James took a loan of $4000 at the rate of 10% simple interest per annum. If he paid an amount of $6800 to clear the loan, then find the time period of the loan.

(4) Calculate the amount due if Robert borrowed a sum of $3100 at 10% simple interest for 3 years.

(5) In how much time a principal of $3000 will amount to $3360 at a simple interest of 3% per annum?

(6) Jessica took a loan of $5500 at the rate of 7% simple interest per annum. If he paid an amount of $9350 to clear the loan, then find the time period of the loan.

(7) Mark took a loan of $6800 at the rate of 8% simple interest per annum. If he paid an amount of $10608 to clear the loan, then find the time period of the loan.

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

(9) What amount does James have to pay after 5 years if he takes a loan of $3000 at 6% simple interest?

(10) Matthew took a loan of $6400 at the rate of 10% simple interest per annum. If he paid an amount of $11520 to clear the loan, then find the time period of the loan.