Question

Linda deposits $50,000 into an account that pays 6% interest per year, compounded annually. Bob deposits $50,000 into an account that also pays 6% per year. But it is simple interest. Find the interest Linda and Bob earn during each of the first three years. Then decide who earns more interest for each year. Assume there are no withdrawals and no additional deposits. Year First Second Third Interest Linda earns (Interest compounded annually) Interest Bob earns (Simple interest) Who earns more interest? Linda earns more. Bob earns more. They earn the same amount. Linda earns more. Bob earns more. They earn the same amount. Linda earns more. Bob earns more. They earn the same amount.

Answer 1

Linda earns $9550.8 interest and bob earns $9000 interest

Explanation:

Linda takes compound interest: C.I. = Principal (1 + Rate)Time − Principal

interest= 50,000(1+6/100)³

=59550.8 - 50000

Linda earns $9550.8 interest in 3 years.

bob takes simple interest: S.I = prt/100

interest = 50,000*6*3/100

Bob earns $9000 in 3 years.

thus, Linda earns more interest than bob.

Answer 2

Explanation:

To calculate the interest earned by Linda for the first year, we can use the formula:

A = P(1 + r/n)^(nt)

Where A is the amount after t years, P is the principal amount, r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the time in years.

For the first year, we have:

A = $50,000(1 + 0.06/1)^(1*1) = $53,000

So, the interest earned by Linda for the first year is:

Interest = $53,000 - $50,000 = $3,000

For the second year, we can use the same formula with t = 2:

A = $50,000(1 + 0.06/1)^(1*2) = $56,180

Interest = $56,180 - $53,000 = $3,180

For the third year, we can use the same formula with t = 3:

A = $50,000(1 + 0.06/1)^(1*3) = $59,468.80

Interest = $59,468.80 - $56,180 = $3,288.80

Now, to calculate the interest earned by Bob for each of the first three years, we can use the formula:

Interest = Prt

Where P is the principal amount, r is the annual interest rate, and t is the time in years.

For the first year, we have:

Interest = $50,0000.061 = $3,000

For the second year, we have:

Interest = $50,0000.061 = $3,000

For the third year, we have:

Interest = $50,0000.061 = $3,000

As we can see, Linda earns more interest than Bob for each year, as her interest is compounded annually, while Bob's interest is simple interest. Therefore, the answer is:

Linda earns more.