Question

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?

Answer 1

The answer is "75,000"

Step-by-step explanation:

Initial Price = 3000

Sales price=15000

Time= 30 years

`\to 15000= 3000 * (1+r)^(30) \\\\\to (15000)/(3000 )= (1+r)^(30)\\\\\to 5= (1+r)^(30)\\\\\to 5^{(1)/(30)}= (1+r)^{30 * (1)/(30)}\\\\\to 5^{(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 * 100\\\\\to r \% = 5.511306\\\\\to \text{The next 30 years' estimated price :}\\\\`

`\to 15000 * (1+ 5.511306 \%)^(30)\\\\\to 15000 * (1+ (5.511306)/(100))^(30)\\\\ \to 15000 * (1+ 0.05511306)^(30)\\\\ \to 15000 * (1.05511306)^(30)\\\\ \to 15000 * 4.9999995\\\\ \to 74,999.9925\\\\\to \bold{75,000}`