Question

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)

Answer 1

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