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?
i = .0275/12 = .002291666...
what is 5700(1.00229166..)^144 ?
To calculate the future value of the savings account after 12 years, we can use the formula for compound interest:
Future Value = P (1 + r/n)^(nt)
Where:
P = principal amount (the original deposit)
r = annual interest rate (in decimal form)
n = number of times the interest is compounded per year
t = number of years
In this case:
P = $5,700
r = 2.75% (or 0.0275 as a decimal)
n = 12 (monthly compounding)
t = 12 (12 years)
Plugging in the values into the formula, we get:
Future Value = 5700(1 + 0.0275/12)^(12*12)
Calculating the exponent first, we have:
Future Value = 5700(1.0022917)^(144)
Next, we raise the base to the power:
Future Value ≈ 5700 * 1.424437086
Finally, multiplying the original deposit by the result, we get:
Future Value ≈ $8,125.44
Therefore, the original deposit of $5,700 will grow to approximately $8,125.44 in 12 years when placed in the savings account earning a 2.75% APR compounded monthly.
To determine how much the original deposit will grow to in 12 years, you can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the final amount
P = the principal (initial deposit)
r = annual interest rate (as a decimal)
n = number of times interest is compounded per year
t = number of years
In this case, the principal (P) is $5,700, the annual interest rate (r) is 2.75% (or 0.0275 as a decimal), the interest is compounded monthly, so the number of times compounded per year (n) is 12, and the number of years (t) is 12.
Plugging in these values into the formula:
A = 5700(1 + 0.0275/12)^(12*12)
Now you can calculate the final amount (A) using a calculator or a spreadsheet software.
A ≈ $7,715.30
Therefore, the original deposit of $5,700 will grow to approximately $7,715.30 in 12 years.