Question

Kristin opens a savings account with $3500. She deposits $2400 every year into the account that has a 0.65% interest rate, compounded quarterly. If she doesn't withdraw any money, what will the account balance be in 10 years?

1. $28551.51
2. $24776.39
3. $28511.25
4. $24816.65
I don't know what formula to use or how to solve.

Answer 1

To find the account balance for this question you have to use the formula of a compound interest and the formula of the future value of an annuity ordinary.

The formula of a compound interest is
A=p (1+r/k)^kt
A future value?
P present value 3500
R interest rate 0.0065
K compounded quarterly 4
T time 10 years

Also the formula of the future value of an annuity ordinary is
Fv=pmt [(1+r/k)^(kt)-1)÷(r/k)]
Fv future value?
PMT since the payment per year is 2400 so you should find the payment per quarter which is 600 (2400÷4) because the interest is quarterly.
R interest rate 0.0065
K compounded quarterly 4
T time 10 years

The sum of those two formulas is the answer.
The balance is
3,500×(1+0.0065÷4)^(4×10)
+600×(((1+0.0065÷4)^(4
×10)−1)÷(0.0065÷4))
=28,511.25.....answer