Problema Solution
If you want to save $25,000 for a down payment on a house and you have ten years to save this amount, how much would you need to save monthly to achieve this goal if the interest rate is 5% compounded monthly, and also 8%.
Answer provided by our tutors
We are dealing with ordinary annuity
S = $25,000 is the future value
t = 10 years
r = 0.05 or 5% the annual interest rate
m = 12 is the number of compounding periods per year compounded monthly (12 months in a year)
n = m*t = 12*10 = 120 is the number of periods
i = r/m = 0.05/12 is the interest rate per period
R = ? the periodic monthly payment
S = R[((1 + i)^n - 1)/i]
R = S/[((1 + i)^n - 1)/i]
R = 25000/[((1 + 0.05/12)^120 - 1)/(0.05/12)]
R = $161 monthly payment
click here to see the solution
if r = 0.08 or 8% the annual interest rate we will have
i = r/m = 0.08/12 is the interest rate per period
R = 25000/[((1 + 0.08/12)^120 - 1)/(0.08/12)]
R = $136.65 monthly payment
click here to see the solution