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) Joseph took a loan of $5400 at the rate of 6% simple interest per annum. If he paid an amount of $8316 to clear the loan, then find the time period of the loan.

(2) Barbara took a loan of $5100 at the rate of 9% simple interest per annum. If he paid an amount of $9231 to clear the loan, then find the time period of the loan.

(3) Betty took a loan of $6500 at the rate of 8% simple interest per annum. If he paid an amount of $11180 to clear the loan, then find the time period of the loan.

(4) What amount will be due after 2 years if Matthew borrowed a sum of $3600 at a 8% simple interest?

(5) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 6% simple interest?

(6) What amount does Charles have to pay after 5 years if he takes a loan of $3900 at 6% simple interest?

(7) Calculate the amount due if Barbara borrowed a sum of $3550 at 3% simple interest for 3 years.

(8) Michael took a loan of $4600 at the rate of 7% simple interest per annum. If he paid an amount of $6532 to clear the loan, then find the time period of the loan.

(9) Anthony took a loan of $6600 at the rate of 9% simple interest per annum. If he paid an amount of $10164 to clear the loan, then find the time period of the loan.

(10) If Karen paid $4266 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.