Simple Interest
Math MCQs

Question :    Betty took a loan of $6500 at the rate of 6% simple interest per annum. If he paid an amount of $10010 to clear the loan, then find the time period of the loan.

Correct Answer  9

Solution & Explanation

Solution

Given,

Principal (P) = $6500

Rate of Simple Interest (R) = 6% per annum

Amount (A) = $10010

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 = $10010 – $6500 = $3510

Thus, Simple Interest = $3510

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 × 3510}/_{6500 × 6}

= ³⁵¹⁰⁰⁰/₃₉₀₀₀

= 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) = $6500

Rate of Simple Interest (R) = 6% per annum

Simple Interest = $3510 (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 = 6% of Principal

= 6% of $6500

= ⁶/₁₀₀ × 6500

= ^{6 × 6500}/₁₀₀

= ³⁹⁰⁰⁰/₁₀₀ = 390

Thus, simple Interest for 1 year = $390

Now,

∵ If the simple Interest is $390, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₃₉₀ years

∴ If the simple Interest is $3510, then the time = ¹/₃₉₀ × 3510 years

= ^{1 × 3510}/₃₉₀ years

= ³⁵¹⁰/₃₉₀ = 9 years

Thus, time (T) = 9 years Answer

Similar Questions

(1) Margaret took a loan of $6700 at the rate of 10% simple interest per annum. If he paid an amount of $11390 to clear the loan, then find the time period of the loan.

(2) If Linda borrowed $3350 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.

(3) Calculate the amount due if John borrowed a sum of $3200 at 2% simple interest for 3 years.

(4) Calculate the amount due after 9 years if Jessica borrowed a sum of $5750 at a rate of 6% 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) Christopher took a loan of $6000 at the rate of 7% simple interest per annum. If he paid an amount of $9780 to clear the loan, then find the time period of the loan.

(7) How much loan did Timothy borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8140 to clear it?

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

(9) What amount does Mary have to pay after 5 years if he takes a loan of $3050 at 5% simple interest?

(10) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 5% simple interest for 7 years.