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30 March, 22:06

You have $1000 to invest in two different accounts. In order to save the money you need for college, you need to average 6.6 percent interest. If the two accounts pay 5 percent and 7 percent interest, how much should you invest in each account?

a) $500 in 5%, $500 in 7%

b) $400 in 5%, $600 in 7%

c) $200 in 5%, $800 in 7%

d) $800 in 5%, $200 in 7%

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  1. 30 March, 22:16
    0
    a) $500 + $525 = $ 1,025

    b) $420 + $642 = $ 1,062

    c) $210 + $856 = $ 1,066

    d) $840 + $214 = $ 1,056

    Step-by-step explanation:

    Compound Interest Equation

    A = P (1 + r/n) ^nt

    Where:

    A = Accrued Amount (principal + interest)

    P = Principal Amount

    I = Interest Amount

    R = Annual Nominal Interest Rate in percent

    r = Annual Nominal Interest Rate as a decimal

    r = R/100

    t = Time Involved in years, 0.5 years is calculated as 6 months, etc.

    n = number of compounding periods per unit t; at the END of each period

    Compound Interest Formulas and Calculations:

    Calculate Accrued Amount (Principal + Interest)

    A = P (1 + r/n) ^nt

    Calculate Principal Amount, solve for P

    P = A / (1 + r/n) ^nt

    Calculate rate of interest in decimal, solve for r

    r = n[ (A/P) ^1/nt - 1]

    Calculate rate of interest in percent

    R = r * 100

    Calculate time, solve for t

    t = ln (A/P) / n[ln (1 + r/n) ] = [ ln (A) - ln (P) ] / n[ln (1 + r/n) ]
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