Question

Damian invested $880 in an account paying an interest rate of 5.2% compounded

annually. Assuming no deposits or withdrawals are made, how long would it take, to the nearest tenth of a year, for the value of the account to reach $1,290?

Answer 1

Explanation:

880×1.052^t = 1290

1.052^t = 1290/880 = 129/88

t ≅ 7.5 years

Answer 2

• 7.5 years

Explanation:

Given:

• Investment P = $880
• Interest rate r = 5.2% = 0.052 times
• Compound number n = 1 (annual)
• Time t = ?
• Final amount A = $1290

The equation is below, solve for t:

• A = P(1 + r/)^(nt)
• 1290 = 880(1 + 0.052)^t
• 1.052^t = 1290/880
• 1.052^t = 1.4659
• t = log 1.4659 / log 1.052
• t = 7.5 years (rounded)