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Interest rate. In​ 1972, Bob purchased a new Datsun 240Z for ​$3,000. Datsun later changed its name to​ Nissan, and the 1972 Datsun 240Z became a classic. Bob kept his car in excellent condition and in 2002 could sell the car for seven times what he originally paid. What was​ Bob's annualized rate of return for the 30 years he owned this​ car? If he keeps the car for another thirty years and earns the same​ rate, what could he sell the car for in​ 2032? What was​ Bob's annualized rate of return for the 30 years he owned this​ car?

Respuesta :

Answer:

The answer is "75,000"

Explanation:

Initial  Price = 3000  

Sales price=15000  

Time= 30 years  

[tex]\to 15000= 3000 \times (1+r)^{30} \\\\\to \frac{15000}{3000 }= (1+r)^{30}\\\\\to 5= (1+r)^{30}\\\\\to 5^{\frac{1}{30}}= (1+r)^{30 \times \frac{1}{30}}\\\\\to 5^{\frac{1}{30}}= (1+r)^{1}\\\\\to 5^{0.0333333333}= (1+r)^{1}\\\\\to 1.05511306= (1+r)\\\\\to 1.05511306-1=r\\\\\to r= .05511306\\\\\to r \% = 05511306 \times 100\\\\\to r \% = 5.511306\\\\\to \text{The next 30 years' estimated price :}\\\\[/tex]

[tex]\to 15000 \times (1+ 5.511306 \%)^{30}\\\\\to 15000 \times (1+ \frac{5.511306}{100})^{30}\\\\ \to 15000 \times (1+ 0.05511306)^{30}\\\\ \to 15000 \times (1.05511306)^{30}\\\\ \to 15000 \times 4.9999995\\\\ \to 74,999.9925\\\\\to \bold{75,000}[/tex]

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