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Natasha2012 [34]

2 years ago

6

cynthia invests some money in a bank which pays 5% compound interest per year. She wants it to be worth over £8000 at the end of

3 years. what is the smallest amount, to the nearest pound she can invest

1 answer:

exis [7]2 years ago

6 0

Answer:

The smallest amount is $\£6,911$

Step-by-step explanation:

we know that

The compound interest formula is equal to

$A=P(1+\frac{r}{n})^{nt}$

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

in this problem we have

$t=3\ years\\ A=\£8,000\\ r=5\%=5/100=0.05\\n=1$

substitute in the formula above

$8,000=P(1+\frac{0.05}{1})^{1*3}$

solve for P

$8,000=P(1.05)^{3}$

$P=8,000/(1.05)^{3}$

$P=\£6,910.70$

Round to the nearest pound she can invest

The smallest amount is $\£6,911$

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