What future amount of money will be accumulated 10 years from now by investing $1500 now...

What future amount of money will be accumulated 10 years from now by investing $1500 now plus $5500 4 years from now at 6% interest compounded semi-annually?

Expert Solution

$1500 is invested now (t = 0) and 5500 is invested 4 years from now (t = 4 or semi-annual period of 8). This cash flow is shown using the below table:

Semi-annual period	0	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20
Cash flow	1500								5500

Semi-annual interest rate = r = 6%/2 = 3%Annual imterest rate = 6%

Since it is a semi-annual compound interest So, cash flow at the end of 4 years happens at the semi-annual period of 8 (4*2)

Total no. of semi-annual periods = n = 10*2 = 20

We need to calculate the future value of cash flows at t=0 and t= 4, 10 years from now

Future value of $1500 at [t = 10 or n = 20] is given by FV₁ = 1500*(1+3%)²⁰ = 2709.1669

Future value of $5500 at [t = 10 or n = 20] is given by FV₂ = 5500*(1+3%)¹² = 7841.6849

Total value at the end of 10 years = FV₁+FV₂ = 2709.1669 + 7841.6849 = 10550.8517

Answer -> 10550.85 (Rounded to 2 decimal places)

jeff jeffy answered 5 months ago

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