Suppose you deposit ​$1500 in a savings account that pays interest at an annual rate of ​4%. If no money is added or withdrawn from the​ account, answer the following questions.

Question

a. How much will be in the account after 4 ​years?

b. How much will be in the account after 17 ​years?

c. How many years will it take for the account to contain ​$2500​?

Answer 1

Use the equation:

where A(t) is the amount you have in savings at any time "t", A0 is the amount at time t = 0, which is 1500 in this case, and "r" is the rate of interest in decimal form, so in this case that is 0.04 (4% = 0.04).

So for a) A(4) = 1500(1 + 0.04)⁴ = 1500(1.04)⁴ = 1500(1.16986) = $1754.79

Repeat this process for question b)

For question c) solve the following for "t":

2500 = 1500(1 + 0.04)^t

2500/1500 = 1.04^t

5/3 = 1.04^t

To solve for "t", take the log of both sides:

log(5/3) = log(1.04^t)

One of the properties of logarithms is that you can bring an exponent on the interior of the log out front as a multiplier:

log(5/3) = t•log(1.04)

log(5/3)/log(1.04) = t

Plug this into your calculator to get t = 13.02 or rounding off, t = 13 years