Question

Theo deposited $1,250 in a savings account that pays 6% interest,compounded quarterly. What was his balance at the end of the secondquarter after the interest had been added?a. $1,270.31b. $1,270.65c. $1,290.62d. $1,287.78

Answer 1

d. $1,287.78

Step-by-step explanation:

The formula for the compound interest is

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

where

A = final amount

P = principle (inital) amount

r = interest rate / 100

n = number of times interest is applied per time period

t = time.

Now in our case

P = 1250

r = 6/ 100 = 0.06

n = 4 (quarterly)

t = 2 quarters = 0.5 of a year

therefore, we have

`A=1250(1+(0.06)/(4))^(4\cdot0.5)`

which simplifies to give

`\boxed{A=1287.78}`

Hence, at the end of the second quarter, Theo's balance would be 1287.78, and therefore, choice D is the correct answer.