Question

Zoe invested $780 in an account paying an interest rate of 5.7% compounded daily. Assuming no deposits or withdrawals are made, how long would it take, to the nearest year, for the value of the account to reach $1,230?

Answer 1

8 years

Explanation:Given

Investment P = $780

Interest rate r = 5.7% = 0.057 annually compounded daily

Number of compounds n = 365

Final amount A = $1230

Time t = x

Required formula

A = P(1 + r/n)ⁿˣ

Substitute values and solve for x

1230 = 780(1 + 0.057/365)³⁶⁵ˣ

1.05865ˣ = 1230/780

1.05865ˣ = 1.57692

x = log 1.57692 / log 1.05865

x = 8 years

Answer 2

• 8 years

Explanation:

Given

• Investment P = $780
• Interest rate r = 5.7% = 0.057 annually compounded daily
• Number of compounds n = 365
• Final amount A = $1230
• Time t = x

Required formula

• A = P(1 + r/n)ⁿˣ

Substitute values and solve for x

• 1230 = 780(1 + 0.057/365)³⁶⁵ˣ
• 1.05865ˣ = 1230/780
• 1.05865ˣ = 1.57692
• x = log 1.57692 / log 1.05865
• x = 8 years