## Rae deposit 6,000 into a savings account with an interest rate of 4% compounded monthly. how long will it take for the account to be worth 1

Question

Rae deposit 6,000 into a savings account with an interest rate of 4% compounded monthly. how long will it take for the account to be worth 10,000?

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1 month 2021-09-11T10:55:29+00:00 1 Answer 0

1. Answer: it will take 13.3 years

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 = 6000

A = 10000

r = 4% = 4/100 = 0.04

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

Therefore,.

10000 = 6000(1 + 0.04/12)^12 × t

10000/6000(1 + 0.0033)^12t

1.67 = 1.0033^12t

Taking log to base 10 of both sides, it becomes

Log 1.67 = 12tLog 1.0033

0.223 = 12t × 0.0014

0.223 = 0.0168t

t = 0.223/0.0168

t = 13.3 years