Question

The apr of deloris' savings account is 3.8%, and interest is compounded semiannually. if the principal in deloris' savings account were $13,700 for an entire year, what would be the balance of her account after all the interest is paid for the year?

Answer 1

The future value of the balance in a savings account, PV, with an apr of r% compounded t times a year for n years is given by:


`FV=PV\left(1+ (r)/(t) \right)^(nt)`

Given that the apr of deloris' savings account is 3.8%, and interest is compounded semiannually. if the principal in deloris' savings account were $13,700 for an entire year, the balance of her account after all the interest is paid for the year is given by


`FV=13,700\left(1+ (0.038)/(12) \right)^(12*1) \\ \\ 13,700(1+ 0.0032)^(12)=13,700(1.0032)^(12) \\ \\ 13,700(1.0387)=\bold{\$14,229.76}`

Answer 2

Deloris' account balance would be $14,225.55 after one year.

Step-by-step explanation:

The formula
`FV=PV(1+(r)/(n))^(nt)` is used to find compound interest.

FV = result or final amount

PV = starting or principal amount

r = annual interest rate (as a fraction)

n = number of compounds a year (semiannually is 2, quarterly is 4...)

t = number of years

Now we can plug and solve:

`FV=13,700(1+(0.038)/(2))^(2(1))` =
`13,700(1+0.019)^2` =
`13,700(1.019)^2` =
`13,700(1.038361)`

= $14,225.55