Final answer:
Geoff's savings will grow to GBP 10000 in approximately 14.2 years, reaching this amount in the year 2032, given a monthly compound interest rate of 0.3%. None of the provided options (2020, 2021, 2022, or 2023) is correct.
Step-by-step explanation:
Geoff wants to know when his savings account, with a starting balance of GBP 5500 and a monthly interest rate of 0.3%, will grow to reach GBP 10000. To solve this, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the amount of money accumulated after n years, including interest.
P = the principal amount (the initial amount of money).
r = the annual interest rate (decimal).
n = the number of times that interest is compounded per year.
t = the number of years the money is invested.
Since the interest is compounded monthly, n = 12. The monthly interest rate of 0.3% is equivalent to an annual rate of 3.6% (0.3% x 12), so r = 0.036. We need to find the value of t that satisfies the equation:
10000 = 5500(1 + 0.036/12)^(12t)
Solving for t, we find that it takes approximately 14.2 years, meaning that Geoff's savings would reach GBP 10000 in the year 2032, which is not one of the provided options.