Question

Colin invests £2900 into his bank account.

He receives 3% per year compound interest.
How much will Colin have after 4 years?
Give your answer to the nearest penny where appropriate.

Answer 1

$3264

Step-by-step explanation:

`\sf compound \ interest : P(1+(r)/(100) )^n`
"P" is principal, "r" is rate of interest, "n" is time (years)

Here given:

• principal: £2900

• rate of interest: 3%

• time: 4 years

After 4 years amount:

`\rightarrow \sf 2900(1+(3)/(100))^4`

`\rightarrow \sf 2900(1.03)^4`

`\rightarrow \sf 3263.9755`

`\rightarrow \sf 3264` (rounded to nearest whole number)

Answer 2

£3263.98 (nearest penny)

Step-by-step explanation:

Compound interest formula

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

where:

• A = final amount
• P = principal
• r = interest rate (in decimal form)
• n = number of times interest applied per time period
• t = number of time periods elapsed

Given:

• P = £2900
• r = 3% = 0.03
• n = 1
• t = 4

Substituting given values into the formula and solving for A:

`\implies \sf A=2900(1+(0.03)/(1))^(1 * 4)`

`\implies \sf A=2900(1.03)^(4)`

`\implies \sf A=3263.975549`

Therefore, Colin will have £3263.98 after 4 years (to the nearest penny).