Calculate the following

Question

Calculate the accumulated value of the following investments at their given rates and compounding periods. Write out the formula being used to calculate these accumulated amounts showing the substitution of values. Round all final answer only to the nearest dollar. Don’t round intermediate values. a.)a.

A.$12,[email protected]%, compounded quarterly for 20 years

B.$23,000@2% compounded weekly for 25 years

C, $12,[email protected]% compounded continuously for 20 years

D, $23,000@2% compounded continuously for 25 years

Answer 1

12.5K, 3.5% 1/4ly compounding for 20 years

FV = PV(1+r/n)^nt where n=4 = # of compounding periods per year, t = # of years=20, r=APR = 3.5%=.035, PV = Present Value = $12,500, FV = Future Value of investment in 20 years from now

FV = 12.500(1+.035/4)^4(20) =about $25,095.38 rounded to nearest penny

= $25,095 rounded to nearest dollar

B) $23000 2% compounded weekly for 25 years

FV = 23000(1+.02/52)^52(25) = about $37,917

C) is same as A) except with continuous compounding

FV = PVe^rt = 12500e^80 = about $6.957778 x10^38

= $695,777,800,000,000,000,000,000,000,000,000,000,000, a modern miracle of compound interest. You're rich rich rich and broke the bank maybe about $696 undecillion (eleven-tillion or in lay terms a "bazillion" a really Big number up there in the stratosphere). Halleluia Amen. King Tut was never so rich. but a "tiny" mistake,

re work the numbers to get

FV = 12500e^.035(20), not ^80 which was not for A

= 12500(2.718281828^.7 = about $25,172

D) $23000 2% 25 years, continuous compounding

FV = 23,000e^.02(25) = 23000e^.5 = about $37,921