find the accumulated value of an investment of 25,000 for 4 years at an interest rate of 5%, if the money is a compounded semiannually; b. coumpounded quaterly; c. compounded monthly d. coumpounded continuously.

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I'll try the first one. The remaining cases are similar and serve as exercises for you (as they should).

Principal, P = 25000

Period, t = 6 months.

Time, T = 4 years.

Number of periods, n = 4/0.5=8

Annual interest rate, = 5%

Interest rate per period, i = 5%*0.5=2.5%

Future value (compound interest)

= P(1+i)^n

= 25000*(1+2.5%)^8

= 25000*1.2184

= $30,460.07

Principal, P = 25000

Period, t = 6 months.

Time, T = 4 years.

Number of periods, n = 4/0.5=8

Annual interest rate, = 5%

Interest rate per period, i = 5%*0.5=2.5%

Future value (compound interest)

= P(1+i)^n

= 25000*(1+2.5%)^8

= 25000*1.2184

= $30,460.07

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