Question

If a savings account of $49,400 is compounded semi-annually at 5.07 % annual interest, how much will the account be worth in 32months? Round your answer to the nearest cent, if necessary. Note: 365 days in a year and 30 days in a month.

Answer 1

`\$56,465.63`

Step-by-step explanation

Parameters given:

Principal = $49,400

Rate = 5.07% = 0.0507

Time = 32 months = 2.67

Number of times compounded per year = 2

To find the amount after 32 months, we apply the compound amount formula:

`A=P(1+(r)/(n))^(nt)`

P = principal

r = rate

n = number of times compounded per year

t = number of years

Therefore, the amount after 32 months is:

`\begin{gathered} A=49,400(1+(0.0507)/(2))^((2\cdot2.67)) \\ A=49400(1+0.02535)^(5.34) \\ A=49400(1.02535)^(5.34) \\ A=\$56,465.63 \end{gathered}`