<p>Assume that 1 year from now you plan to deposit $1000 in a savings account th

Question

<p>Assume that 1 year from now you plan to deposit $1000 in a savings account that pays a nominal rate of 8%. (a). If the bank compounds interest annually, how much will you have in your account 4 years from now.</p>
<p>(b) What would your balance be 4 years from now if the bank used quarterly compounding rather than annual compounding?</p>
<p>(c) Suppose you deposited the $1000 in 4 payments of $250 each at the year 1,2,3, and 4. How much would you have in your account at the end of Year 4, based on 8% annual compounding?</p>
<p>(d) Suppose you deposited 4 equal payments in your account at the end of Years 1,2,3, and 4. Assuming an 8% interest rate, how large would each of your payments have to be for you to obtain the same ending balance as you calculated in part a?</p>

Explanation / Answer

a) 1000(1+8/100)^4=1360.48 b)1000(1+8/100*4)^4*4=12143.83 c)250(1.08)+[250+250(1.08)](1.08)^2+[[250+250(1.08)](1.08)^2](1.08)^3+[[[250+250(1.08)](1.08)^2](1.08)^3](1.08)^4=2680.06 d)250(1.08)+[250+250(1.08)](1.08)^2=876.52, we need 483.48 more, at the end of 3 years, 250(1.08)+[250+250(1.08)](1.08)^2+[[250+250(1.08)](1.08)^2](1.08)^3=1640 we receive, in 3rd year , 1640-876.52=763.48 we get therefore 483.48/763.48=0.63 years i.e., to get 1360.48 we need to deposit for 2.63 years

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