Mathematics and investment

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1. Angelo wants to renovate his house in 3 years. He estimates the cost 300,000. How much must Angelo invest now at 8% compounded quarterly in order to have 300,000 3 years from now.
2. Angelo Ancis want to save 500,000 in 5.5 years to renovate their rest house. If the bank is paying 8% interest, compounded quarterly. How much must they deposit now in order to have money for the project?
3. Brian bought second hand truck for 125,000. He made down payment of 5,000 and agree to pay the balance in 24 equal monthly payments. If interest charge was 8% compounded monthly. How much brian should pay each month.
4. A debt of 25,000 was repaid in 10 equal quarterly payments. If the rate of interest was 7% compounded quarterly. What was the size if each payment.
5. RCBC bank pays an interest rate 4% annually compounded quarterly. How much money will CJ have in the bank at the end of 5 years if he deposits 2,500 at the end of each quarter?

  • Mathematics and investment -

    1. P = Po(1+r)^n

    P = $300,000

    Po = Initial investment.

    r = (8%/4)/100% = 0.02 = Quarterly % rate expressed as a decimal.

    n = 4Comp/yr. * 3yrs. = 12 Compounding
    periods.

    P = Po*(1.02)^12 = 300,000
    Po = 300,000/1.02^12 = $236,547.95

    2. Same procedure as #1.

    3. Po = 125,000 - 5000 = $120,000 =
    Initial balance.

    P = (Po*r*t)/(1-(1+r)^-t)

    r = (8%/12)/100% = 0.006667 = Monthly %
    rate.

    t = 2yrs. * 12mo/yr. = 24 mo.

    Plug the above values into the given Eq
    and get:
    P = $130,254.60

    Amount/mo. = P/t

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