If an individual saves $5,700 and elects to place the total dollar amount into a savings account earning 2.75% APR compounded monthly, how much will the original deposit grow to in 12 years?
what is 5700(1.0275)^12 ?
An individual saves 5700 elects to
Place the total dollars into savings earning 2.75% apr compound monthly how much will the original deposit grow in 12 years.
To calculate the future value of a savings account with compound interest, you can use the formula:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment
P = the principal amount (initial deposit)
r = the annual interest rate (in decimal form)
n = the number of times that interest is compounded per year
t = the number of years
In this case:
P = $5,700
r = 2.75% = 0.0275 (in decimal form)
n = 12 (compounded monthly)
t = 12 years
Substituting the values into the formula:
A = $5,700 * (1 + 0.0275/12)^(12*12)
Calculating this:
A ≈ $5,700 * (1 + 0.0023)^(144)
A ≈ $5,700 * (1.0023)^(144)
A ≈ $5,700 * 1.39244104
Rounding to the nearest dollar:
A ≈ $7,938
Therefore, the original deposit will grow to approximately $7,938 in 12 years.