Annual deposits of $3150 are made into a bank account earning 4 % interest per year. Round all answers to two decimal places
(a) What is the balance in the account right after the 15th deposit if interest is calculated annually?
For this I know the formula is
A = P(1 + R/N)^Nt
A = 3150( 1 + 0.04/1)^1(15)
A = 5,672.97
(b) What is the balance in the account right after the 15th deposit if interest is calculated continuously?
For this I know the formula is
A = Pe^rt
A = 3150e^(0.03 x 15)
A = 4,940.18
sorry, no. Your formulas are for ONE deposit at the start, not for annual deposits.
Look up "amount of a sinking fund"
S = 3150[ 1.04^n - 1 ] /.04
You get e^rt for EACH deposit for its time t
3150 [ e^14(.04) + e^13(.04) + ....e^.04]
I am sorry I do not know an easy way to do that
The formulas are for the END of the year
so do it for 14 years, then add that 15th deposit of 3150 (tricky wording)
(a) To calculate the balance in the account right after the 15th deposit if interest is calculated annually, you can use the formula:
A = P(1 + R/N)^Nt
Where:
A = the final balance in the account
P = the annual deposit amount
R = the interest rate (in decimal format)
N = the number of times interest is compounded per year
t = the number of years
In this case, the annual deposit amount (P) is $3150, the interest rate (R) is 4% (0.04 in decimal format), the number of times interest is compounded per year (N) is 1, and the number of years (t) is 15.
Plugging in these values into the formula, we get:
A = 3150(1 + 0.04/1)^1(15)
Calculating this, we find that the balance in the account right after the 15th deposit, if interest is calculated annually, is $5,672.97.
(b) To calculate the balance in the account right after the 15th deposit if interest is calculated continuously, you can use the formula:
A = Pe^rt
Where:
A = the final balance in the account
P = the annual deposit amount
e = the mathematical constant approximately equal to 2.71828
r = the interest rate (in decimal format)
t = the number of years
In this case, the annual deposit amount (P) is $3150, the interest rate (r) is 4% (0.04 in decimal format), and the number of years (t) is 15.
Plugging in these values into the formula, we get:
A = 3150e^(0.04 x 15)
Calculating this, we find that the balance in the account right after the 15th deposit, if interest is calculated continuously, is $4,940.18.