Henry invested $59,000 in an account paying an interest rate of 2% compounded quarterly. Assuming no deposits or withdrawals are made, how much money, to the nearest cent, would be in the account after 20 years?

Answer 1

To calculate the final amount in the account after 20 years with 2% interest compounded quarterly, we can use the formula for compound interest:

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

Where:
A = the amount of money accumulated after n years, including interest
P = the principal amount (initial investment)
r = the annual interest rate (decimal)
n = the number of times that interest is compounded per year
t = the number of years the money is invested for

Plugging in the given values:
P = $59,000
r = 2% = 0.02
n = 4 (quarterly compounding)
t = 20 years

A = $59,000(1 + 0.02/4)^(4*20)
A = $59,000(1 + 0.005)^80
A = $59,000(1.005)^80
A = $59,000(2.20804)
A = $130,099.36

Therefore, after 20 years, there would be approximately $130,099.36 in the account.

Answer 2

this is wrong

Answer 3

I apologize for the mistake. Let's recalculate the final amount in the account after 20 years using the correct formula for compound interest:

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

Where:
A = the amount of money accumulated after n years, including interest
P = the principal amount (initial investment)
r = the annual interest rate (decimal)
n = the number of times that interest is compounded per year
t = the number of years the money is invested for

Given:
P = $59,000
r = 2% = 0.02
n = 4 (quarterly compounding)
t = 20 years

A = $59,000(1 + 0.02/4)^(4*20)
A = $59,000(1 + 0.005)^80
A = $59,000(1.005)^80
A = $59,000 * 2.191594
A = $129,302.45

Therefore, after 20 years, there would be approximately $129,302.45 in the account.