Financial Mathematics pdf free download

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Financial Mathematics pdf free download. Exercise (a)
Fund A is invested at an effective annual interest rate of 3%. Fund B is invested at an
effective annual interest rate of 2.5%. At the end of 20 years, the total in the two funds
is 10,000. At the end of 31 years, the amount in Fund A is twice the amount in Fund B.
Calculate the total in the two funds at the end of 10 years.
Solution (a)
Let the initial funds be A and B. Therefore, we have two equations and two unknowns:
A(1.03)20 + B(1.025)20 = 10, 000
A(1.03)31 = 2B(1.025)31
Solving for B in the second equation and plugging it into the first equation gives us A =
3, 624.73 and B = 2, 107.46. We seek A(1.03)10 + B(1.025)10 which equals
3, 624.73(1.03)10+2, 107.46(1.025)10 = 7, 569.07
Exercise (b)
Carl puts 10,000 into a bank account that pays an annual effective interest rate of 4% for
ten years. If a withdrawal is made during the first five and one-half years, a penalty of 5%
of the withdrawal amount is made. Carl withdrawals K at the end of each of years 4, 5, 6,
7. The balance in the account at the end of year 10 is 10,000. Calculate K.
Solution (b)
10, 000(1.04)10 − 1.05K(1.04)6 − 1.05K(1.04)5 −K(1.04)4 −K(1.04)3 = 10, 000
14, 802 −K[(1.05)(1.04)6 + (1.05)(1.04)5 + (1.04)4 + (1.04)3] = 10, 000
4, 802 = K · 4.9→ K = 980

Financial Mathematics pdf free download

Financial Mathematics pdf free download

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