Colin invests £2350 into a savings account. The bank gives 4.2% compound interest for the first 4 years and 4.9% thereafter. How much will Colin have after
10 years to the nearest pound?

£3691 (nearest pound)

Step-by-step explanation:

Consider the rate of compound interest is r and the initial amount of savings is P, hence

Therefore, the final amount of savings after nth years of compund interest is

.

Given that 4.2% compound interest was used for the first 4 years to a savings of £2350, thus

Then, taking the final amount of savings previously into an initial amount for the next 6 years with 4.9% compound interest.

, and

for

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

note the following:

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for