A bank account was opened with a deposit of $2750 at an APR of 3.5% compounded one of the following ways. Find the amount in this account after 6 years with compounding of:
(round answers to nearest 100th)
annually: $
semi-annually: $
quarterly: $
monthly: $
weekly: $
daily: $
1000 times a year: $
10,000 times a year: $
I will do one of them for you, you do the others
Quarterly:
i = .035/4 = .00875
n = 6(4) = 24
amount = P(1 + i)^n
= 2750(1.00875)^24
= $ 3389.52
Correct... If you look closely, you can also find the formula that "Reiny" uses, which is the key to solving the problems you have.
Okay so for weekly and daily, im not getting an answer
To find the amount in the account after a certain number of years with different compounding frequencies, we can use the compound interest formula:
A = P(1 + r/n)^(nt)
where:
A = the final amount in the account
P = the principal amount (initial deposit)
r = annual interest rate (in decimal form)
n = number of times the interest is compounded per year
t = number of years
Given:
P = $2750
r = 3.5% = 0.035
Now, let's calculate the amount in the account after 6 years with different compounding frequencies:
1. Annually (n = 1):
A = 2750(1 + 0.035/1)^(1*6)
A ≈ 2750(1.035)^6
A ≈ $3252.89
2. Semi-annually (n = 2):
A = 2750(1 + 0.035/2)^(2*6)
A ≈ 2750(1.0175)^12
A ≈ $3273.64
3. Quarterly (n = 4):
A = 2750(1 + 0.035/4)^(4*6)
A ≈ 2750(1.00875)^24
A ≈ $3285.28
4. Monthly (n = 12):
A = 2750(1 + 0.035/12)^(12*6)
A ≈ 2750(1.002917)^72
A ≈ $3290.58
5. Weekly (n = 52):
A = 2750(1 + 0.035/52)^(52*6)
A ≈ 2750(1.000673077)^312
A ≈ $3292.48
6. Daily (n = 365):
A = 2750(1 + 0.035/365)^(365*6)
A ≈ 2750(1.00009589)^2190
A ≈ $3292.77
7. 1000 times a year (n = 1000):
A = 2750(1 + 0.035/1000)^(1000*6)
A ≈ 2750(1.000034999)^6000
A ≈ $3292.97
8. 10,000 times a year (n = 10000):
A = 2750(1 + 0.035/10000)^(10000*6)
A ≈ 2750(1.0000034999999)^60000
A ≈ $3293.02
Therefore, rounded to the nearest hundredth, the amounts in the account after 6 years with different compounding frequencies are:
- Annually: $3252.89
- Semi-annually: $3273.64
- Quarterly: $3285.28
- Monthly: $3290.58
- Weekly: $3292.48
- Daily: $3292.77
- 1000 times a year: $3292.97
- 10,000 times a year: $3293.02