Thirty years ahead of retirement Eric opened a savings account that earns a 5% i

Question

Thirty years ahead of retirement Eric opened a savings account that earns a 5% interest rate compounded continuously and contributed to this account at the annual rate of exist900 per year for 30 years. Ten years ahead of retirement, Jozef opened a similar savings account that earns a 5% interest rate compounded continuously and decided to quadruple the annual rate of contributions to to exist3600 per year for 10 years. Who has more money in their savings account at retirement? (Assume that the contributions are made continuously and into the accounts.) has more money in his or her account at retirement. Eric Jozel

Explanation / Answer

Conitnuously compounded of periodic payment is given by:

A = P*(e^(rt) - 1)/(e^r - 1)

for Eric

P1 = $900

r = 5% = 0.05

t = 30 years

A1 = 900*[(e^(0.05*30) - 1)/(e^0.05 - 1)]

A1 = $61116.69

for Jozef

P2 = $3600

r = 5% = 0.05

t = 10 years

A2 = 3600*[(e^(0.05*10) - 1)/(e^0.05 - 1)]

A1 = $45549.96

So Eric will have more money in Saving Account.

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