Asked by Myisha Garfield on Jul 21, 2024
Verified
James and Terry open a savings account that has a 2.75% annual interest rate,compounded monthly.They deposit $500 into the account each month.How much will be in the account after 20 years?
A) $48,407.45
B) $159,744.59
C) $330,600.15
D) $580,894.18
Compounded Monthly
Refers to the process of calculating interest on both the initial principal and the accumulated interest from previous periods on a monthly basis.
- Derive future savings amounts by considering different compounding cycles.
- Ascertain the future worth of ongoing payments into savings vehicles.
Verified Answer
VK
vishruth keshireddyJul 26, 2024
Final Answer :
B
Explanation :
To solve this problem, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
where:
A = the amount in the account after t years
P = the initial deposit or principal (in this case, $0)
r = the annual interest rate (2.75%)
n = the number of times the interest is compounded per year (12, for monthly)
t = the number of years (20)
We also know that James and Terry deposit $500 into the account each month, which means that the effective monthly deposit is $1,000 (since there are two of them).
Plugging in the values, we get:
A = 0(1 + 0.0275/12)^(12*20) + (1000*12)*( (1 + 0.0275/12)^(12*20) - 1)/(0.0275/12)
A = $159,744.59
Therefore, the best choice is B.
A = P(1 + r/n)^(nt)
where:
A = the amount in the account after t years
P = the initial deposit or principal (in this case, $0)
r = the annual interest rate (2.75%)
n = the number of times the interest is compounded per year (12, for monthly)
t = the number of years (20)
We also know that James and Terry deposit $500 into the account each month, which means that the effective monthly deposit is $1,000 (since there are two of them).
Plugging in the values, we get:
A = 0(1 + 0.0275/12)^(12*20) + (1000*12)*( (1 + 0.0275/12)^(12*20) - 1)/(0.0275/12)
A = $159,744.59
Therefore, the best choice is B.
Learning Objectives
- Derive future savings amounts by considering different compounding cycles.
- Ascertain the future worth of ongoing payments into savings vehicles.