Question

NO LINKS!! URGENT HELP PLEASE!!

1. Suppose you make a deposit of $4000 into an investment account that earns 8% interest compounded monthly. What is the account worth after 5 years?

2. An overdue credit card has a balance of $460. The credit card company is charging 21.5% interest, compounded daily. What is the balance on the credit card after 2 years (assuming no payments were made)?

Answer 1

1. $5,959.38

2. $707.05

Explanation:

`\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}}`

Question 1

Given values:

• P = $4,000
• r = 8% = 0.08
• n = 12 (monthly)
• t = 5 years

Substitute the given values into the compound interest formula and solve for A:

`\implies A=4000\left(1+(0.08)/(12)\right)^(12 \cdot 5)`

`\implies A=4000\left(1.0066666...\right)^(60)`

`\implies A=4000\left(1.48984570...\right)`

`\implies A=5959.38283...`

Therefore, the account is worth $5,959.38 after 5 years.

Question 2

Given values:

• P = $460
• r = 21.5% = 0.215
• n = 365 (daily)
• t = 2 years

Substitute the given values into the compound interest formula and solve for A:

`\implies A=460\left(1+(0.215)/(365)\right)^(365 \cdot 2)`

`\implies A=460\left(1.00058904...\right)^(730)`

`\implies A=460\left(1.53706292...\right)`

`\implies A=707.048946...`

Therefore, the balance on the credit card after 2 years (assuming no payments were made) is $707.05.

Answer 2

1.$5959.38

2. $707.05

Explanation:

1.

To find the account balance after 5 years with a principal of $4000 and 8% interest compounded monthly, we use the formula for compound interest:

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

where:

P = $4000 (principal)

r = 8% per year (annual interest rate)

n = 12 (compounding periods per year, as interest is compounded monthly)

t = 5 (number of years)

Plugging in the values, we get:

A = $4000 * (1 + 0.08/12)^(12*5)

= $5959.38 (rounded to 2 decimal places)

Therefore, the account is worth $5959.38 after 5 years.

2.

To find the balance on a credit card with a balance of $460 and 21.5% interest compounded daily after 2 years, we use the formula for compound interest:

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

where:

P = $460 (principal)

r = 21.5% per year (annual interest rate)

n = 365 (compounding periods per year, as interest is compounded daily)

t = 2 (number of years)

Plugging in the values, we get:

A = $460 * (1 + 0.215/365)^(365*2)

= $707.045(rounded to 3 decimal places)

Therefore, the balance on the credit card after 2 years is $707.05.