Question

Gianna has a two $3,000 one year CDs at different banks. Each compounds

interest at a rate of 8.4%. One bank compounds the interest monthly while the
other compounds interest daily. What would be the difference in the ending
balances of both CDs after one year?*
A) $2.29
B) $1.53
C) $1.17
D) $0.93

Answer 1

Option D

Explanation:

To calculate compound interest we will use the formula :

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

Where,

A = Amount on maturity

P = Principal amount = $3000

r = rate of interest = 8.4% = 0.084

n = number of compounding period = Monthly = 12

t = time = 1 year

Now put the values in the formula.

`A=3000(1+(0.08)/(12))^((12)(1))`

=
`3000(1+0.007)^(12)`

= 3000(1.007)¹²

= 3000 × 1.08731066

= 3261.93198 ≈ $3261.93

While the other bank compounds interest daily.

Therefore, n = 365

Now put the values in the formula with n = 365

`=3000(1+(0.084)/(365))^((365)(1))`

`=3000(1+0.00023014)^(365)`

`=3000(1.00023014)^(365)`

= 3000 × 1.08761958

= 3262.85874 ≈ $3262.86

Difference in the ending balance = 3262.86 - 3261.93

= $0.93

The difference in the ending balances of both CDs after one year would be $0.93.