Question

Fernando has a savings account balance of $2,471.23. The interest rate on the account is 2.4% compounded quarterly. If he opened the account nine years ago, what was the value of his initial deposit?

Answer 1

You will need a formula for compound interest solved for principal. (See attached).
Principal = $2,471.23 / (1+ (.024/4)^4*9

Principal = $2,471.23 / 1.2403016056
Principal = $1,992.44
(I checked this with an online compound interest calculator to check this - it is correct.)

Answer 2

The initial deposit was $1992.44.

Explanation:

Compound interest formula is :

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

Fernando has a savings account balance of $2,471.23.

Means A = 2471.23

r = 2.4% = 0.024

n = 4

t = 9

Putting the values in formula we get;

`2471.23=p(1+(0.024)/(4))^(4*9)`

=>
`2471.23=p(1+(0.024)/(4))^(36)`

=>
`2471.23=p(1.006)^(36)`

=>
`2471.23=p(1.24030)`

=> p = 1992.44

Hence, the initial deposit was $1992.44.