Can someone please help. How log will it take you to save $100,000 if you start saving 1597 every 3 months starting today? Assume and interest rate of 6% compounded quarterly.
Business Calculator
py/cy= 4
I=6%
fv= 100,000
1597= PMT
BGN is on
To calculate the time it will take to save $100,000 by saving $1597 every 3 months with an interest rate of 6% compounded quarterly, you can use the future value of an annuity formula.
The formula for the future value of an annuity is:
FV = PMT * [(1 + r)^n - 1] / r
Where FV is the future value, PMT is the payment amount, r is the interest rate per period, and n is the number of periods.
In this case, PMT = $1597, r = 6% (or 0.06 as a decimal), and FV = $100,000. Since the payments are made every 3 months, and the interest is compounded quarterly, the number of periods is 4 times the number of years.
Using the business calculator information you provided:
Set "py/cy" (payments per year / compounding periods per year) to 4.
Set "I" (interest rate) to 6%.
Set "fv" (future value) to $100,000.
Set "PMT" (payment amount) to $1597.
Make sure "BGN" (beginning payment indicator) is on, as the payments start today.
Once you have input these values, you can calculate the number of periods (n) by rearranging the formula:
n = log(1 + (FV * r) / PMT) / log(1 + r)
Using the business calculator, input the values obtained:
n = log(1 + ($100,000 * 0.06) / $1597) / log(1 + 0.06)
Solving this equation will yield the number of periods (n), which represents the number of quarters it will take to save $100,000.
This calculation can be simplified by using a financial calculator or a spreadsheet software with built-in financial functions, such as Excel. Alternatively, there are online financial calculators available that can perform these calculations for you.