Colin invests £2350 into a savings account. The bank gives 4.2% compound interest for the first 4 years and 4.9% thereafter. How

Question

DENIUS

9 days ago

10

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?

Mathematics

1 answer:

zzz [4K] · Answer 1 · 2026-02-24T00:32:59+03:00

To tackle this, we will apply the compound interest formula: $A=P(1+ \frac{r}{n} )^{nt}$
where
$A$ represents the final amount after $t$ years
$P$ denotes the initial investment
$r$ is the interest rate expressed as a decimal
$n$ indicates the frequency of interest compounding annually

Initially, for the first four years, we have: $P=2350$ , $r= \frac{4.2}{100} =0.042$ , $t=4$ , and as the problem does not specify the frequency of compounding, we will assume it occurs annually; thus, $n=1$ . Now, let's insert these values into our formula:
$A=P(1+ \frac{r}{n} )^{nt}$
$A=2350(1+ \frac{0.042}{1} )^{(1)(4)}$
$A=2350(1+0.042)^{4}$
$A=2770.38$

For the subsequent six years, the initial amount will be the resulting figure from our prior calculation, which means $P=2770.38$ . We also know that: $r= \frac{4.9}{100} =0.049$ , $t=6$ , and $n=1$ . Let's substitute these figures back into our formula:
$A=P(1+ \frac{r}{n} )^{nt}$
$A=2770.38(1+ \frac{0.049}{1})^{(1)(6)$
$A=2770.38(1+0.049)^6$
$A=3691.41$

In conclusion, Collin's account will contain <span>£3691.41 after a decade.</span>