Question

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%

Answer 1

Answer:

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)]