Question

Ellen has recently inherited $5200, which she wants to deposit into a savings account. She has determined that her two best bets are an account that compounds monthly at an annual rate of 3.3% (Account 1) and an account that compounds daily at an annual rate of 4.8% (Account 2).

Step 1 of 2 : Which account would pay Ellen more interest?

Account 1 or Account 2

Answer 1

technically you really don't need to do any math to solve this (the account that compounds at a higher rate **and** more often gives more total interest)

but demonstrating mathematically:

A = P(1 + r/n)^(nt)
where P is the principal, r is the interest rate as a decimal, n is the # of times compounded per year, t is time in years

for account 1: A = P(1 + r/n)^(nt) = 5200(1 + 0.033/12)^(12*t)

for account 2: A = 5200(1 + 0.048/365)^(365t)

that 365t exponent makes account 2 multiply much faster

Answer 2

ohhh that makes sense

Answer 3

How much would Ellen's balance be from Account 2 over 2.5 years? Round to two decimal places.

Answer 4

account 2: A = 5200(1 + 0.048/365)^(365t), where t = 2.5

A = 5200(1 + 0.048/365)^(365*2.5)

Answer 5

5325.94442208 ⋅ 0.5^x^2

Answer 6

I would just chuck this whole line into a calculator if you can

5200(1 + 0.048/365)^(365*2.5) = 5862.94

Answer 7

thank you , that's correct

Answer 8

Martha invests $7800 in a new savings account which earns 5.1% annual interest, compounded semi-annually. What will be the value of her investment after 5 years? Round to the nearest cent.

Answer 9

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

P = 7800
semi-annually --> n = 2
r = 0.051
t = 5

A = 7800(1 + 0.051/2)^(2*5)

Answer 10

41016.3

Answer 11

check your input again

A = 7800(1 + 0.051/2)^(2*5)

A = 7800(1.0255)^(10) = 10033.47

Answer 12

$10033.47 ?

Answer 13

yes

Answer 14

thank you