# : Bill Smith, age 25, begins to make yearly deposits of \$1600 into his IRS account that pays interest at a quarterly rate of 8% compounded..?

BillSmith, age 25, begins to make yearly deposits of \$1600 into his IRS account that pays interest at a quarterly rate of 8% compounded continuously. How much will he have in her bank account if he retires at age 70?

^^How do you use the annuity formula for this? A0= M; An= (1+r/N)An-1 + P

where A0= initial amount

P=principal

r=rate

N= # times a year

Please explain step by step if possible. Thank you! TEN POINTS FOR A CORRECT ANSWER :)

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• Anonymous
6 years ago

Pf = Pi*(1 + r/n)^(nt)

t = 45, n = 4, plug in the rest

Pi + Pi*r = Pi*(1 + r) .....principal with interest once

Pi + Pi*r + r(Pi + Pi*r) = Pi + Pi*r + Pi*r + Pi*r^2 = Pi(1 + r)^2....principal with interest twice

When interest is compounded the problem becomes complicated. The IRS account is compounded with a quarterly interest, that is a quarter of the interest is paid separately but within an entire year.

Pi + Pi*r/n = Pi(1 + r/n)....compounded interest first time

Pi + Pi*r/n + r/n*(Pi + Pi*r/n) = Pi(1 + r/n)^2...compounded interest second time

We have a pattern here, that is we've noticed that Pf = Pi(1 + r/n)^n but if we replace (1 + r/n)^n to b and ask ourselves how the money will grow when at the end of time t, this becomes Pf = Pi*b^t or Pi*(1 + r/n)^nt

• Arianna6 years agoReport

does this problem work with the annuity formula though? thanks ^

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• Amount at age 70 = \$1600* e^ (0.08*(70-25)

= \$58,557.18

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