Question

Minnie deposited $5,375 into a savings account 18 years ago. The account has an interest rate of 3.2% and the balance is currently $9,561.39. How often does the interest compound?

Answer 1

What have you tried?

Answer 2

I tried it using the compound formula
A=P(1+r/n)^nt
and got the answer wrong. Am I using the wrong formula? @tkhunny

Answer 3

Ift it compounds annually, I got $9476 from your formula, close.

You could try some other common compounding practices, such as twice a year, which gave $9518. Getting loser.

Answer 4

Monthly?

Answer 5

I calculated it quarterly and got an almost similar answer. I got $9,539.55 . Can you do it and see if you got the same answer as me? @douglaswinslowcooper

Answer 6

I got 9539.74, almost identical. Go to 6 times a year or better 12 times a year.

Answer 7

12 per year gave me 9554.
Radical move: 365 times a year, daily,

Bingo: $9561

Answer 8

There is an exponential function for truly continuous
compounding, exp(something). That may be what was sought.
We got close.

Answer 9

A/P = exp[(0.032)(t)]

That gives $9561.63,

which may be what they wanted you to do.

Answer 10

Good night.

Answer 11

A trip down logical paths, using existing compounding periods, may solve the problem.

First, let's see if it's even possible.
Annual -- n = 1 -- $9,475.74 Lowest Possible
Continuous -- n = \(\infty\) -- $9,561.63 Highest Possible
Good, the desired answer is between those. It's pretty close to the Continuous, so I suspect it will require rather frequent compounding.

Semi-Annual -- n = 2 -- $9,518.14
Quarterly -- n = 4 -- $9,539.75
Monthly -- n = 12 -- $9,554.31
Weekly -- n = 52 -- $9,559.94
Daily -- n = 365 -- $9,561.39
There it is!