 Mathematics
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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Answers (1)
1. 30 March, 22:16
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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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