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 $9230 to clear the loan, then find the time period of the loan.

Correct Answer  7

Solution & Explanation

Solution

Given,

Principal (P) = $6500

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

Amount (A) = $9230

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 = $9230 – $6500 = $2730

Thus, Simple Interest = $2730

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 × 2730}/_{6500 × 6}

= ²⁷³⁰⁰⁰/₃₉₀₀₀

= 7 years (using formula)

Thus, Time (T) = 7 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 = $2730 (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 $2730, then the time = ¹/₃₉₀ × 2730 years

= ^{1 × 2730}/₃₉₀ years

= ²⁷³⁰/₃₉₀ = 7 years

Thus, time (T) = 7 years Answer

Similar Questions

(1) Lisa took a loan of $6100 at the rate of 10% simple interest per annum. If he paid an amount of $12200 to clear the loan, then find the time period of the loan.

(2) 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.

(3) Barbara took a loan of $5100 at the rate of 7% simple interest per annum. If he paid an amount of $8313 to clear the loan, then find the time period of the loan.

(4) What amount will be due after 2 years if Mark borrowed a sum of $3700 at a 10% simple interest?

(5) How much loan did William borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6050 to clear it?

(6) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 8% simple interest for 4 years.

(7) Michael took a loan of $4600 at the rate of 9% simple interest per annum. If he paid an amount of $7084 to clear the loan, then find the time period of the loan.

(8) What amount does Elizabeth have to pay after 5 years if he takes a loan of $3450 at 5% simple interest?

(9) In how much time a principal of $3150 will amount to $3780 at a simple interest of 5% per annum?

(10) What amount does Joseph have to pay after 5 years if he takes a loan of $3700 at 3% simple interest?