Question

john invested $2000 that earn interest at 4% per annum compounded monthly. two year later the interest rate is 4.50% compounded quaterly. determine the accumulated value of investment two year after the change

Answer 1

`\$2,369.11`

Explanation:

we know that

The compound interest formula is equal to

`A=P(1+(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

Part 1)

`t=2\ years\\ P=\$2,000\\ r=0.04\\n=12`

substitute in the formula above

`A=2,000(1+(0.04)/(12))^(12*2)`

`A=2,000(1.0033)^(24)`

`A=\$2,166.29`

Part 2)

`t=2\ years\\ P=\$2,166.29\\ r=0.045\\n=4`

substitute in the formula above

`A=2,166.29(1+(0.045)/(4))^(4*2)`

`A=2,166.29(1.01125)^(8)`

`A=\$2,369.11`