Emma invested $41,000 in an account paying an interest rate of 2.6% compounded monthly. 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 $49,300?

Question

Mathematics

Sneakers

27 September, 02:34

Emma invested $41,000 in an account paying an interest rate of 2.6% compounded monthly. 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 $49,300?

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Answers (1)

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Roland · Answer 1

Answer: it will take 7 years for the value of the account to reach $49,300

Step-by-step explanation:

We would apply the formula for determining compound interest which is expressed as

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

Where

A = total amount in the account at the end of t years

r represents the interest rate.

n represents the periodic interval at which it was compounded.

P represents the principal or initial amount deposited

From the information given,

P = $41000

A = $49300

r = 2.6% = 2.6/100 = 0.026

n = 12 because it was compounded 12 times in a year.

Therefore,

49300 = 41000 (1 + 0.026/12) ^12 * t

49300/41000 = (1 + 0.0022) ^12t

1.2024 = (1.0022) ^12t

Taking log of both sides of the equation, it becomes

Log 1.2024 = 12t * log 1.0022

0.08 = 12 * 0.00095 = 0.0114t

t = 0.08/0.0114

t = 7 years