Mathematics of Finance

Kang Kar SG

Hello all,

Have questions regarding Mathematics of Finance

Compound Interest:
If money is worth 5% compounded continously, what payments X at the end of 8 months and 2X at the end of 2 years will equitably replace the obligations: $30000 due now and $20000 with interest from today at 6% compounded daily due in 3 years?

Ans: X= $18225.51

What I did was:

30000e^(-0.06x3) + 20000e^(0.06x3) = A

Xe^[0.05x(-2/3)] + 2Xe^[0.05x(-2)] = A

From there can get A but does not tally the answer, which step did I do wrongly? Please advise

Annuity:
Shipping Engineering Ltd. has deposited $1000000 at end of each year into an investment plan for the last 12 years. The deposits earned interest at 6% compounded annually for the first 4 years; at 5.5% compounded annually for the next 5 years; and 6.4% compounded annually for the last 3 years.

a) What is the accumulated value of his investment plan? (Ans: $16800588.91)

What I did from the understanding of the question:
1000000[(1.06^4)-1/0.06] = A
A[(1.055^5)-1/0.055) = B
B[(1.064^3)- 1/0.064) = C (answer)

Which part did I do wrongly? Please advise

Kang Kar SG

Annuity:
A unit of landed property, valued at $2,000,000, is sold for $400,000 down. The buyer agrees to pay the balance with interest compounded monthly by paying $50,000 monthly as long as necessary, the first payment due 3 years from now. The interest rate is 6%.

a. Find the number of $50,000 payments needed. (Ans: 42)

b. Find the size of the concluding payment one month after the last $50,000 payment.
(Ans: $18895.31)

a) Not (2000000 - 400000) / 50000 ?

b) Not sure how to approach

Please advise, thank you :)