Simple Interest
Math MCQs

Question :    Margaret took a loan of $6700 at the rate of 9% simple interest per annum. If he paid an amount of $12730 to clear the loan, then find the time period of the loan.

Correct Answer  10

Solution & Explanation

Solution

Given,

Principal (P) = $6700

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

Amount (A) = $12730

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 = $12730 – $6700 = $6030

Thus, Simple Interest = $6030

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 × 6030}/_{6700 × 9}

= ⁶⁰³⁰⁰⁰/₆₀₃₀₀

= 10 years (using formula)

Thus, Time (T) = 10 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) = 9% per annum

Simple Interest = $6030 (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 $6700

= ⁹/₁₀₀ × 6700

= ^{9 × 6700}/₁₀₀

= ⁶⁰³⁰⁰/₁₀₀ = 603

Thus, simple Interest for 1 year = $603

Now,

∵ If the simple Interest is $603, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₆₀₃ years

∴ If the simple Interest is $6030, then the time = ¹/₆₀₃ × 6030 years

= ^{1 × 6030}/₆₀₃ years

= ⁶⁰³⁰/₆₀₃ = 10 years

Thus, time (T) = 10 years Answer

Similar Questions

(1) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 3% simple interest for 7 years.

(2) How much loan did Jacob borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8800 to clear it?

(3) What amount will be due after 2 years if Anthony borrowed a sum of $3650 at a 4% simple interest?

(4) Calculate the amount due after 10 years if Linda borrowed a sum of $5350 at a rate of 5% simple interest.

(5) John took a loan of $4400 at the rate of 6% simple interest per annum. If he paid an amount of $5984 to clear the loan, then find the time period of the loan.

(6) Mark took a loan of $6800 at the rate of 8% simple interest per annum. If he paid an amount of $12240 to clear the loan, then find the time period of the loan.

(7) Calculate the amount due if Barbara borrowed a sum of $3550 at 5% simple interest for 4 years.

(8) What amount will be due after 2 years if Daniel borrowed a sum of $3550 at a 10% simple interest?

(9) Mary had to pay $3416 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(10) If Kimberly paid $5022 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.