Question

Calculate the accumulated value of an investment of 1,250 after 8 years assuming the annual effective rate of discount is 4% for the first 3 years, the annual nominal rate of interest compounded monthly 9% for the next 2 years and force of interest is 2.5% for the final 3 years. Answer to the nearest cent.

Answer 1

The formula for the next three years is=PV*(1+r)^n=1250*(1+4%)^3=1250*(1.04^3)=$1406.08

Now, for the next two years, we have to monthly compound it.

The value for the next two years=$1406.08*(1+(r/12))^(n*12)=$1406.08*(1+(9%/12))^(2*12)=$1406.08*(1.0075)^24=$1682.25

For the next three years, its force of interest which is continuous compounding.

The formula is=PV*(e^rt)

e is the mathematical constant approximated as 2.7183

The accumulated value=$1682.25*(e^(2.5%*3))=$1682.25*(2.7183)^(2.5%*3)=$1813.27