Xavi looks at his account and notices that if the current monthly interest rate stays constant he is expected to have $33,000 in 6 years (i.e. once 6 years have elapsed) and $68,000 in 9 years. (15 points) a) How much money does he have now (at time 0)? (5 points) b) If his predictions are correct, except after 7 years, the nominal rate halves and then stays at that value, how much money will he have in 9 years? Assume the interest rate is compounded monthly. (10 points)
Ans A)
Lets assume that Xavi invested amount X in his account and then
following condition holds
X(1+(r%/12))^72=33000
X(1+(r%/12))^108=68000
(1+(r%/12))^36=2.0606
(1+(r%/12))=2.0606^(1/36)
r%/12=2.0286% is the monthly rate
We now can find X=33000/(1.020286)^72=7772.042
He has now X=$7772.04
Ans B)
In other case nominal rates halves after 7 years therefore
estimation can be calculated as below
7772.04(1.020286)^84(1.010143)^24=$53501.45
In 2nd case we will have $53501.45 after 9 years
Xavi looks at his account and notices that if the current monthly interest rate stays constant...
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