Question

NO LINKS!! URGENT HELP PLEASE!!!

1. You are comparing two different investment accounts. You plan to deposit a balance of $5000 for 8 years. Compare the plans below and decide which investment account is best.

Plan A: Earns 6% interest per year, compounded quarterly (4 times a year).

Plan B: Earns 5% interest per year, compounded daily.

Answer 1

Plan A is the best investment account.

Explanation:

To determine which of the two different investments accounts is the best, substitute the given values for each account into the compound interest formula and compare the final account balances.

`\boxed{\begin{minipage}{8.5 cm}\underline{Compound Interest Formula}\\\\$ A=P\left(1+(r)/(n)\right)^(nt)$\\\\where:\\\\ \phantom{ww}$\bullet$ $A =$ final amount \\ \phantom{ww}$\bullet$ $P =$ principal amount \\ \phantom{ww}$\bullet$ $r =$ interest rate (in decimal form) \\ \phantom{ww}$\bullet$ $n =$ number of times interest is applied per year \\ \phantom{ww}$\bullet$ $t =$ time (in years) \\ \end{minipage}}`

Given Plan A values:

• P = $5,000
• r = 6% = 0.06
• n = 4 (quarterly)
• t = 8 years

Plan A balance:

`\implies A=5000\left(1+(0.06)/(4)\right)^(4 \cdot 8)`

`\implies A=5000\left(1.015\right)^(32)`

`\implies A=8051.62160...`

Therefore, the balance of the Plan A account is $8,051.62.

Given Plan B values:

• P = $5,000
• r = 5% = 0.05
• n = 365 (daily)
• t = 8 years

Plan B balance:

`\implies A=5000\left(1+(0.05)/(365)\right)^(365 \cdot 8)`

`\implies A=5000\left(1..00013698...\right)^(2920)`

`\implies A=7458.9191...`

Therefore, the balance of the Plan B account is $7,458.92.

Plan A is the best investment account since you will earn $592.70 more investing in this account than if investing the same amount of money for the same amount of time in the Plan B account.

Answer 2

Plan A: which earns 6% interest compounded per year, compounded quarterly.

Explanation:

To determine which plan is the best investment option, we need to calculate the final balance of each plan after 8 years and compare them.

Plan A:

With a 6% interest rate compounded quarterly, the formula to calculate the final balance after n years is given by:

A = P * (1 + r/m)^(m*n)

Where:

P = $5000 (the initial deposit)

r = 0.06 (the annual interest rate as a decimal)

m = 4 (number of times compounded per year)

n = 8 (number of years)

Plugging in the values, we get:

A = $5000 * (1 + 0.06/4)^(4 * 8)

A = $8051.62

Plan B:

With a 5% interest rate compounded daily, the formula to calculate the final balance after n years is given by:

A = P * (1 + r/365)^(365*n)

Where:

P = $5000 (the initial deposit)

r = 0.05 (the annual interest rate as a decimal)

n = 8 (number of years)

Plugging in the values, we get:

A = $5000 * (1 + 0.05/365)^(365 * 8)

A = $7458.919

After calculating the final balance for each plan, it is clear that Plan A is the better option as it results in a higher balance of $8051.62 compared to Plan B's balance of $7458.919. So, if you are depositing $5000 for 8 years, it is best to choose Plan A, which earns 6% interest compounded per year, compounded quaterly.