Question

You currently have $5,400. First United Bank will pay you an annual interest rate of 8.9, while Second National Bank will pay you an annual interest rate of 10. How many fewer years must you wait for your account value to grow to $13,900 at Second National Bank?A. 1.06 yearsB. 1.08 yearsC. 1.40 yearsD. 1.17 yearsE. 1.32 years

Answer 1

Answer:

Second National  Bank

Present value (PV) = $5,400

Future value (FV) = $13,900

Interest rate (r) = 10% = 0.10

FV = PV(1 + r)n

$13,900 = $5,400(1 + 0.10)n    

$13,900 = (1.10)n

$5,400            

2.574074074 = (1.10)n

Log 2.574074074 = n  log 1.10

Log 2.574074074 = n  

Log 1.10                  

n =  9.9 years      

None of the answers is correct                                                                                                                                                          

Explanation:

In this case, we will apply the formula of future value of a lump sum. The present value, interest rate and future value were provided with  the exception of number of years. Thus, the number of years becomes the subject of the formula. The future value equals present value, multiplied                     by 1 plus interest rate, raised to power number of years.