Answer:
Balance after 30 years = $151,018.50
Explanation:
In order to calculate this, we will calculate the future value on an amount invested, gaining interest over the years of investment, and this is given by:
[tex]FV = PV (1 + r)^{t}[/tex]
where:
FV = future value
PV = present value
r = interest rate
t = time in years.
Hence the future value is calculated as follows:
1. For the first 10 years at 7% interest:
7% interest = 7/100 = 0.07
[tex]FV = 12,500 (1 + 0.07)^{10}[/tex]
[tex]FV = 12,500 (1.07)^{10}\\FV = 12,500 * 1.967 = 24,589.392[/tex]
2. For the last 20 years at 9.5%(0.095) interest:
Note that for the remaining 20 years, the present value (PV) used = 24,589.392, as ending balance after the first 10 years
[tex]FV = 24,589.392 (1 + 0.095)^{20}[/tex]
[tex]FV = 24,589.392 (1.095)^{20}\\FV= 24,589.392 * 6.1416\\FV = 151,018.496[/tex]
Total Future value earned = $151,018.50
