Simple Interest
Math MCQs

Question :    Barbara took a loan of $5100 at the rate of 7% simple interest per annum. If he paid an amount of $7956 to clear the loan, then find the time period of the loan.

Correct Answer  8

Solution & Explanation

Solution

Given,

Principal (P) = $5100

Rate of Simple Interest (R) = 7% per annum

Amount (A) = $7956

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 = $7956 – $5100 = $2856

Thus, Simple Interest = $2856

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 × 2856}/_{5100 × 7}

= ²⁸⁵⁶⁰⁰/₃₅₇₀₀

= 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) = $5100

Rate of Simple Interest (R) = 7% per annum

Simple Interest = $2856 (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 = 7% of Principal

= 7% of $5100

= ⁷/₁₀₀ × 5100

= ^{7 × 5100}/₁₀₀

= ³⁵⁷⁰⁰/₁₀₀ = 357

Thus, simple Interest for 1 year = $357

Now,

∵ If the simple Interest is $357, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₃₅₇ years

∴ If the simple Interest is $2856, then the time = ¹/₃₅₇ × 2856 years

= ^{1 × 2856}/₃₅₇ years

= ²⁸⁵⁶/₃₅₇ = 8 years

Thus, time (T) = 8 years Answer

Similar Questions

(1) Calculate the amount due after 10 years if Sarah borrowed a sum of $5850 at a rate of 5% simple interest.

(2) What amount will be due after 2 years if Joshua borrowed a sum of $3950 at a 4% simple interest?

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

(4) Nancy took a loan of $6300 at the rate of 8% simple interest per annum. If he paid an amount of $9324 to clear the loan, then find the time period of the loan.

(5) Calculate the amount due after 10 years if William borrowed a sum of $5500 at a rate of 4% simple interest.

(6) What amount will be due after 2 years if Paul borrowed a sum of $3850 at a 6% simple interest?

(7) Calculate the amount due after 10 years if Elizabeth borrowed a sum of $5450 at a rate of 8% simple interest.

(8) What amount will be due after 2 years if Richard borrowed a sum of $3300 at a 9% simple interest?

(9) If Jessica borrowed $3750 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.

(10) In how much time a principal of $3100 will amount to $3286 at a simple interest of 2% per annum?