Neva collect a $5000 bonus on the first of the year. She puts the $5000 into a savings account and continues to add an additional $188 every month into that account. Her account earns 4.2% compounded monthly. HOw much does Neva have in 5 years?
To determine how much Neva will have in 5 years, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the total amount of money (including principal and interest)
P = the principal amount (initial deposit)
r = interest rate (in decimal form)
n = number of times interest is compounded per year
t = number of years
In this case:
P = $5000 (the initial deposit)
r = 4.2% or 0.042 (as a decimal)
n = 12 (interest is compounded monthly)
t = 5 (number of years)
Let's calculate the monthly contribution made by Neva using the formula for the future value of a series:
FV = PMT * ((1 + r)^n - 1) / r
Where:
FV = the future value of the series
PMT = the monthly contribution
r = interest rate (in decimal form)
n = number of times the contribution is made per year
In this case:
PMT = $188
r = 4.2% or 0.042 (as a decimal)
n = 12 (monthly contributions)
Now, let's calculate the future value of the series using the formula mentioned above:
FV = $188 * ((1 + 0.042/12)^(12*5) - 1) / (0.042/12)
FV ≈ $11,023.57
Finally, let's calculate the total amount Neva will have in 5 years by adding the initial deposit to the future value of the series:
Total amount = $5000 + $11,023.57
Total amount ≈ $16,023.57
Therefore, Neva will have approximately $16,023.57 in 5 years in her savings account.