| An investor deposits $19,000 in an account that earns 2.3% interest compounded
ID: 2912437 • Letter: #
Question
| An investor deposits $19,000 in an account that earns 2.3% interest compounded quarterly. The balance in the account after n quarters is given by 4,-19,001 04 -,2.3 19,0000.023 (a) Write the first eight terms of the sequence. (Round your answers to the nearest cent.) A1 19109.25 A2 19219.13 A3-$ 19329.64 A4 19440.78 As 19552.57 A6 19665.00 A7$19778.06 Ag $ 19891.80 (b) Find the balance in the account after 30 years by computing the 120th term of the sequence. (Round your answer to the nearest cent.) A120-$ (c) Is the balance after 20 years twice the balance after 10 years? Explain. O Yes, because interest is accrued at a fixed rate per year O No, because rounding errors cause the balances to vary slightly over time. O No, because the interest rate will increase or decrease over time. O No, because the value of the investment does not increase linearly O Yes, because interest is not paid until the end of the investment period.Explanation / Answer
b) A 120 = 19000 ( 1+ .023 / 4)^30*4
A 120 = 19000 ( 1+.023/4 )^120
A120 = $ 37805.81
c) balance after 20 years = 19000 ( 1 + .023/4 )^20*4
= 30058
balance after 10 years = 19000 ( 1 +.023/4 )^10*4
= 23897.65
so, the balance is not twice that of 10 years as the value does not increase linearly
4th option is correct
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