Suppose you found a CD that pays 5.1% interest compounded monthly for 5 years.
1.If you deposit $11,000 now, how much will you have in the account in 5 years? (Round to the nearest cent.)
$
2.What was the interest earned? (Round to the nearest cent.)
s
3.Now suppose that you would like to have $20,000 in the account in 5 years. How much would you need to
deposit now? (Round to the nearest cent.)
Answer for all three pls!!
To answer these questions, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment
P = the initial principal (deposit amount)
r = the annual interest rate (in decimal form)
n = the number of times interest is compounded per year
t = the number of years
Now let's calculate the answers step by step:
1. To find the value of the account in 5 years with a $11,000 deposit and a 5.1% interest rate compounded monthly, we plug these values into the formula:
A = 11000(1 + 0.051/12)^(12*5)
Calculating this equation, we find that the account will have approximately $13,226.59 after 5 years.
2. To calculate the interest earned, subtract the initial principal from the future value:
Interest earned = $13,226.59 - $11,000 = $2,226.59
So the interest earned is approximately $2,226.59.
3. To find the amount needed to deposit to have $20,000 in the account after 5 years, we need to rearrange the formula and solve for P:
P = A / (1 + r/n)^(nt)
Plugging in the values:
P = 20000 / (1 + 0.051/12)^(12*5)
Solving this equation, we find that you would need to deposit approximately $16,970.72 now to reach $20,000 in 5 years.
To summarize:
1. The amount in the account after 5 years with a $11,000 deposit is approximately $13,226.59.
2. The interest earned is approximately $2,226.59.
3. To have $20,000 in the account after 5 years, you would need to deposit approximately $16,970.72 now.