Simple Interest
Math MCQs

Question :    Barbara took a loan of $5100 at the rate of 9% simple interest per annum. If he paid an amount of $8313 to clear the loan, then find the time period of the loan.

Correct Answer  7

Solution & Explanation

Solution

Given,

Principal (P) = $5100

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

Amount (A) = $8313

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 = $8313 – $5100 = $3213

Thus, Simple Interest = $3213

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 × 3213}/_{5100 × 9}

= ³²¹³⁰⁰/₄₅₉₀₀

= 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) = $5100

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

Simple Interest = $3213 (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 $5100

= ⁹/₁₀₀ × 5100

= ^{9 × 5100}/₁₀₀

= ⁴⁵⁹⁰⁰/₁₀₀ = 459

Thus, simple Interest for 1 year = $459

Now,

∵ If the simple Interest is $459, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₄₅₉ years

∴ If the simple Interest is $3213, then the time = ¹/₄₅₉ × 3213 years

= ^{1 × 3213}/₄₅₉ years

= ³²¹³/₄₅₉ = 7 years

Thus, time (T) = 7 years Answer

Similar Questions

(1) Calculate the amount due if Sarah borrowed a sum of $3850 at 5% simple interest for 3 years.

(2) Betty took a loan of $6500 at the rate of 7% simple interest per annum. If he paid an amount of $10140 to clear the loan, then find the time period of the loan.

(3) Jennifer took a loan of $4500 at the rate of 7% simple interest per annum. If he paid an amount of $6705 to clear the loan, then find the time period of the loan.

(4) Calculate the amount due after 9 years if Patricia borrowed a sum of $5150 at a rate of 8% simple interest.

(5) What amount does Barbara have to pay after 5 years if he takes a loan of $3550 at 8% simple interest?

(6) What amount does Joseph have to pay after 6 years if he takes a loan of $3700 at 10% simple interest?

(7) What amount does Elizabeth have to pay after 5 years if he takes a loan of $3450 at 7% simple interest?

(8) Calculate the amount due if Charles borrowed a sum of $3900 at 10% simple interest for 4 years.

(9) Mark took a loan of $6800 at the rate of 9% simple interest per annum. If he paid an amount of $12920 to clear the loan, then find the time period of the loan.

(10) Calculate the amount due if Patricia borrowed a sum of $3150 at 3% simple interest for 3 years.