Bank deposits

At the end of each quarter, Patti deposits $1,400 into an account that pays 10% interest compounded quarterly. How much will Patti have in the account in three years?

Note: Use tables, Excel, or a financial calculator round your final answer to the nearest whole dollar. (FV of $1, PV of $1, FVA of $1, and PVA of $1).

Correct answer:

x =  19313.77 USD

Step-by-step explanation:

$$\begin{gathered} a=1400\text{USD} \\ p=10\%=\frac{10}{100}=\frac{1}{10}=0.1 \\ n=3\cdot 4=12 \\ r=1+p/4=1+0.1/4=\frac{41}{40}=1.025 \\ {x}_1=a=1400 \\ {x}_2=x_1\cdot r+a=1400\cdot 1.025+1400=2835 \\ {x}_3=x_2\cdot r+a=2835\cdot 1.025+1400=\frac{34447}{8}=4305.875 \\ {x}_4=x_3\cdot r+a=4305.875\cdot 1.025+1400\doteq 5813.5219 \\ {x}_5=x_4\cdot r+a=5813.5219\cdot 1.025+1400\doteq 7358.8599 \\ {x}_6=x_5\cdot r+a=7358.8599\cdot 1.025+1400\doteq 8942.8314 \\ {x}_7=x_6\cdot r+a=8942.8314\cdot 1.025+1400\doteq 10566.4022 \\ {x}_8=x_7\cdot r+a=10566.4022\cdot 1.025+1400\doteq 12230.5623 \\ {x}_9=x_8\cdot r+a=12230.5623\cdot 1.025+1400\doteq 13936.3263 \\ {x}_{10}=x_9\cdot r+a=13936.3263\cdot 1.025+1400\doteq 15684.7345 \\ {x}_{11}=x_{10}\cdot r+a=15684.7345\cdot 1.025+1400\doteq 17476.8528 \\ {x}_{12}=x_{11}\cdot r+a=17476.8528\cdot 1.025+1400\doteq 19313.7742 \\ x=x_{12}=19313.7742=19313.77\text{USD} \end{gathered}$$

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