Simple Interest
Math MCQs

Question :    In how much time a principal of $3050 will amount to $3660 at a simple interest of 5% per annum?

Correct Answer  4

Solution & Explanation

Solution

Given,

Principal (P) = $3050

Rate of Simple Interest (R) = 5% per annum

Amount (A) = $3660

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 = $3660 – $3050 = $610

Thus, Simple Interest = $610

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 × 610}/_{3050 × 5}

= ⁶¹⁰⁰⁰/₁₅₂₅₀

= 4 years (using formula)

Thus, Time (T) = 4 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) = $3050

Rate of Simple Interest (R) = 5% per annum

Simple Interest = $610 (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 = 5% of Principal

= 5% of $3050

= ⁵/₁₀₀ × 3050

= ^{5 × 3050}/₁₀₀

= ¹⁵²⁵⁰/₁₀₀ = 152.5

Thus, simple Interest for 1 year = $152.5

Now,

∵ If the simple Interest is $152.5, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/_152.5 years

∴ If the simple Interest is $610, then the time = ¹/_152.5 × 610 years

= ^{1 × 610}/_152.5 years

= ⁶¹⁰/_152.5 = 4 years

Thus, time (T) = 4 years Answer

Similar Questions

(1) John took a loan of $4400 at the rate of 9% simple interest per annum. If he paid an amount of $7172 to clear the loan, then find the time period of the loan.

(2) How much loan did John borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5720 to clear it?

(3) What amount does Robert have to pay after 5 years if he takes a loan of $3100 at 6% simple interest?

(4) Donald took a loan of $7000 at the rate of 9% simple interest per annum. If he paid an amount of $12040 to clear the loan, then find the time period of the loan.

(5) Betty took a loan of $6500 at the rate of 6% simple interest per annum. If he paid an amount of $9620 to clear the loan, then find the time period of the loan.

(6) Barbara had to pay $3869.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(7) What amount does Elizabeth have to pay after 6 years if he takes a loan of $3450 at 10% simple interest?

(8) How much loan did Ashley borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7860 to clear it?

(9) William took a loan of $5000 at the rate of 6% simple interest per annum. If he paid an amount of $7400 to clear the loan, then find the time period of the loan.

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