Question

Landon opened a savings account with a deposit of $3,786.45. Nine years later, the balance in the account is $5,135.29. If the interest rate is 3.4%, how often does the interest compound?

Answer 1

Hint:

use the formula

A = P(1+r/n)^(n*t)

Answer 2

In this case

P = 3786.45
r = 0.034
t = 9

Answer 3

Plug these values into the formula A = P(1+r/n)^(n*t) to get


A = P(1+r/n)^(n*t)

A = 3786.45(1+0.034/n)^(n*9)

Answer 4

The goal is to find the value of n which makes A equal to 5135.29

Answer 5

Common of values of n are
n = 1 (annual compounding)
n = 2 (semi-annual compounding)
n = 4 (quarterly compounding)
n = 12 (monthly compounding)
n = 365 (daily compounding)

Answer 6

So plug in each value of n listed above into

A = 3786.45(1+0.034/n)^(n*9)

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So for instance, if n = 1, then

A = 3786.45(1+0.034/n)^(n*9)

A = 3786.45(1+0.034/1)^(1*9)

A = 5115.84143581059

A = 5115.84

which is NOT the value of 5135.29, so we must move onto other values of n and check them

Answer 7

This rules out annual compounding as a possible answer choice

Answer 8

does all this make sense?

Answer 9

yes thank you

Answer 10

ok great, glad it does, yw