Mark put $3290 into a bank that offered 3% interest rate compounded monthly. Mark kept the money in this account for 9 years and then moved all this money to a new account that offered 6% interest rate compounded weekly.
Do not round any numbers until you get to an answer.
How much money was in the first account after 9 years?
$
How much money will be in Mark's new account after 8 more years in the new account?
In other words how much money will Mark have after 17 years?
first stage:
i = .03/12 = .0025
n = 9(12) = 108
second stage:
i = .06/52 = .001153846
n = 8(52) = 416
after first stage:
amount = 3290(1.0025)^108 = $4308.33
after 2nd stage:
amount = 3290(1.0025)^108(1.001153846)^416
= $6960.66
To find the amount of money in the first account after 9 years, 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 investment (principle amount)
r = annual interest rate (as a decimal)
n = number of times interest is compounded per year
t = number of years
Given:
P = $3290
r = 3% = 0.03 (as a decimal)
n = 12 (compounded monthly)
t = 9
Plug these values into the formula:
A = 3290(1 + 0.03/12)^(12*9)
A = 3290(1 + 0.0025)^(108)
To get the final answer, calculate the expression inside the parenthesis first:
(1 + 0.0025)^(108) = 1.0025^(108)
Using a calculator, evaluate the power:
1.0025^(108) ≈ 1.299
Now substitute the value back into the original equation:
A = 3290 * 1.299
A ≈ $4271.91
Therefore, the amount of money in the first account after 9 years is approximately $4271.91.
To find the amount of money in the new account after 8 more years (total of 17 years), we'll use the same formula for compound interest:
A = P(1 + r/n)^(nt)
Given:
P = $4271.91 (amount from the first account)
r = 6% = 0.06 (as a decimal)
n = 52 (compounded weekly)
t = 8
Plug these values into the formula:
A = 4271.91(1 + 0.06/52)^(52*8)
Calculating the expression inside the parenthesis first:
(1 + 0.06/52)^(52*8) = 1.00115^(416)
Using a calculator, evaluate the power:
1.00115^(416) ≈ 1.743
Now substitute the value back into the original equation:
A = 4271.91 * 1.743
A ≈ $7446.52
Therefore, after 17 years, Mark will have approximately $7446.52 in his new account.