Nina made two investments: Investment \text{A}Astart text, A, end text has a value of \$50$50dollar sign, 50 at the end of the first year and increases by 8\%8%8, percent per year. Investment \text{B}Bstart text, B, end text has a value of \$60$60dollar sign, 60 at the end of the first year and increases by \$3$3dollar sign, 3 per year. Nina checks the value of her investments once a year, at the end of the year. What is the first year in which Nina sees that investment \text{A}Astart text, A, end text's value exceeded investment \text{B}Bstart text, B, end text's value

6 years

Explanation:

Future value of investment A :

The formula for calculating future value:

FV = P (1 + r)^n

FV = Future value  

P = Present value  

R = interest rate  

N = number of years

Future value of investment B : 60 + (3 x number of years)

In year I, future value of :

Investment A = 50(1.08) = 54

Investment B = 60 + 3 = 63

in year 1, the value of investment B exceeds that of investment A

In year 2, future value of :

Investment A = 50(1.08^2) = 58.32

Investment B = 60 +( 3 x 2)  = 66

In year 2, the value of investment B exceeds that of investment A

In year 3, future value of :

Investment A = 50(1.08^3) = 62.99

Investment B = 60 +( 3 x 3)  =69

In year 3, the value of investment B exceeds that of investment A

In year 4, future value of :

Investment A = 50(1.08^4) = 68.02

Investment B = 60 +( 3 x 4)  =72

In year 4, the value of investment B exceeds that of investment A

In year 5, future value of :

Investment A = 50(1.08^5) = 73.47

Investment B = 60 +( 3 x 5)  =75

In year 5, the value of investment B exceeds that of investment A

In year 6, future value of :

Investment A = 50(1.08^6) = 79.34

Investment B = 60 +( 3 x 6)  = 78

In year 6, the value of investment A exceeds that of investment B

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