Brian invests £1900 into a savings account. The bank gives 3.5% compound interest for the first 2 years and 4.9% thereafter. How much will Brian have after 6 years to the nearest pound?

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calculista calculista · Answer 1 · 2019-07-05T23:52:26+02:00

Answer:

[tex]\£2,465[/tex]

Step-by-step explanation:

we know that

The compound interest formula is equal to

[tex]A=P(1+\frac{r}{n})^{nt}[/tex]

where

A is the Final Investment Value

P is the Principal amount of money to be invested

r is the rate of interest in decimal

t is Number of Time Periods

n is the number of times interest is compounded per year

step 1

Find the final investment for the first two years

we have

[tex]t=2\ years\\ P=\£1,900\\ r=0.035\\n=1[/tex]

substitute in the formula above

[tex]A=\£1,900(1+\frac{0.035}{1})^{1*2}[/tex]

[tex]A=\£1,900(1.035)^{2}[/tex]

[tex]A=\£2,035.33[/tex]

step 2

Find the final investment for the next 4 years

we have

[tex]t=4\ years\\ P=\£2,035.33\\ r=0.049\\n=1[/tex]

substitute in the formula above

[tex]A=\£2,035.33(1+\frac{0.049}{1})^{1*4}[/tex]

[tex]A=\£2,035.33(1.049)^{4}[/tex]

[tex]A=\£2,464.55[/tex]

Round to the nearest pound

[tex]\£2,464.55=\£2,465[/tex]