Exponential Functions

Question

How much would you need to deposit in an account now in order to have $4000 in the account in 10 years? Assume the account earns 5% interest compounded monthly.

Answer:_______

Answer 1

The Compounded Interest Formula is: A = P (1 + r/n)^nt

Where:

A = Final amount = 4000

P = Initial principal = ?

r = interest rate in decimal = 0.05

n = number of times interest apply per period = 12 (monthly)

t = total period = 10 (years)

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

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

P = 4000 / (1 + 0.05/12)^12*10

P = 4000 / (1 + 0.00416667)¹²⁰

P = 4000 / (1.00416667)¹²⁰

P = 4000 / 1.6470101537605859686732271603713

P ≈ 2,428.64

Answer: You would need to deposit $2,428.64 in order to get $4000 in 10 years with a compounded monthly interest of 5%.

Answer 2

The general form of the equation you would use in this situation is:

where A(t) is the amount you have in your account at any time "t", A₀ is the amount you place in the account at time zero (the beginning), "r" is the yearly interest rate in decimal form (5% = 0.05), and "n" is the number of compounding periods per year (monthly means n = 12)

So, in this case you would be solving for A₀

4000 = A₀(1 + (0.05/12))^(12•10)

4000 = A₀(1 + 0.004166667)¹²⁰

4000 = A₀(1.004166667)¹²⁰

4000 = A₀(1.6470095)

A₀ = 4000/1.6470095

A₀ = $2428.64