Question 1137623: On January 1, 2000, $12,400 was deposited into an account that earns 2.55% interest compounded monthly. On January 1, 2010, $1,600 was deposited into the account and the bank changed the interest rate to 2.31% compounded monthly.
On January 1, 2014, $3,800 was withdrawn from the account and the interest rate was lowered to 1.99% compounded monthly.
a.) if no other deposits, withdrawals, or rate changes occur, how much money did the account have on January 1, 2020?
b.) Determine the total interest that was earned from January 1, 2000 to January 1, 2020?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! on january 1, 2000 you deposited 12400 earning 2.55% interest compounded monthly.
on january 1, 2010, you deposited 4600 earning 2.31% compounded monthly.
on january 1, 2014, you withdrew 3800 from the account and the interest rate was lowered to 1.99% compounded monthly.
from january 1, 2000 to january 1, 2010 is 10 years.
f = p * (1 + r) ^ n
f is the future value
p is the present value
r is the interest rate per time period
n is the number of time periods.
your timer periods are months.
for the first segment between january 1, 2000 and january 1, 2010, you get:
p = 12400
n = 10 * 12 = 120 months.
r = 2.55% / 100 = .0255 / 12 = .002125
formula becomes f = 12400 * (1 + .002125) ^ 120 = 15997.39535.
on january 1, 2010, 1600 is added to this to get a total of 17597.39535.
from january 1, 2010 to january 1, 2014, this is invested at the rate of 2.31% compounded monthly.
f = p * (1 + r) ^ n becomes:
f = 17597.39535 * (1 + .0231/12) ^ (4 * 12) = 19299.16978.
on january 1, 2014, 3800 was withdrawn, leaving a balance of 15499.16978
this was invested from january 1, 2014 to january 1, 2020 at the annual rate of 1.99% compounded monthly.
f = p * (1 + r) ^ n becomes:
f = 15499.16978 * (1 + .0199/12) ^ (6 * 12) = 17463.05606.
if i did this right, that should be what's in the account on january 1, 2020.
i double checked through excel and it appears i did it right, at least if i did it right in excel.
i think that's probably the answer you're looking for.
the amount in the account on january 1, 2020 = 17463.05606.
the total interest earned would probably be calculated as follows:
on january 1, 2000 you deposited 12400.
on january 1, 2010, this grew to 15997.39535.
interest earned would be 15997.39535 minus 12400 = 3597.39535.
on january 1, 2010, you had 17597.39535 in the account which grew to 19299.16978 on january 1, 2014.
interest earned would be 19299.16978 minus 17597.39535 = 1701.77443.
on january 1, 2014, you had 15499.16978 which grew to 17463.05606 on january 1, 2020.
interest earned would be 17463.05606 minus 15499.16978 = 1963.88628.
total interest earned was 3597.39535 + 1701.77443 + 1963.88628 = 7263.05606
i double checked this number through excel and it appears it is correct.
your solution should be:
a.) if no other deposits, withdrawals, or rate changes occur, how much money did the account have on January 1, 2020?
the amount in the account should be 17463.05606.
b.) Determine the total interest that was earned from January 1, 2000 to January 1, 2020?
the total interest earned should be 7263.056055.
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