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= 1,000te^-0.3t dollars per year...

If funds are transferred into an account at the rate of R(t) = 1,000te^-0.3t dollars per year for 5 years and the account pays 4% interest compounded continuously, how much will accumulate in the account over a period of 5 years?

FV = INT(0toT) f(t)e^r(T-t) dt

R(t) = 1,000te^-0.3t

f(t) =1,000te^-0.3t

r = 0.04

T = 5

FV = INT (0 to 5)(1,000t)e^0.04(5-t) dt

u = 1000t

dv = e^0.04(5-t) dt

du =

v = e^0.04(5-t) / -0.04 =

FV = 1,000e^-0.04(5-t) (0 to 5) – INT (0 to 5)

FV = INT(0toT) f(t)e^r(T-t) dt

R(t) = 1,000te^-0.3t

f(t) =1,000te^-0.3t

r = 0.04

T = 5

FV = INT (0 to 5)(1,000t)e^0.04(5-t) dt

u = 1000t

dv = e^0.04(5-t) dt

du =

v = e^0.04(5-t) / -0.04 =

FV = 1,000e^-0.04(5-t) (0 to 5) – INT (0 to 5)

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