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Vadim26 [7]
2 years ago
12

You are thinking about buying a savings bond. The bond costs ​57$ today and will mature in 8 years with a value of 114​$. What a

nnual interest rate will the bond​ earn?
Mathematics
1 answer:
iris [78.8K]2 years ago
8 0

Answer:

                                                                                                ,

Step-by-step explanation:

                                   

.

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This is an exponential decay problem.

Using the equation Y = a *(1-rate)^time

where Y is the future value given as 12,000 and a is the starting value given as 13,000.

The rate is also given as 5%.

The equation becomes:

12,000 = 13,000(1-0.05)^x

12,000 = 13,000(0.95)^x

Divide each side by 13000:

12000/13000 = 0.95^x/13000

12/13 = 0.95^x

Use the natural log function:

x = ln(12/13) / ln(0.95)

x = 1.56 years. ( this will equal 12,000

Round to 2 years it will be less than 12000.

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