In: Finance
Find the accumulated value of $4,715 invested for 13 years if the annual effective rate of discount is 5% for the first 7 years and a nominal rate of discount of 3.8% per year compounded bi-monthly (i.e., every two months) is used thereafter
Given
Amount invested = $ 4715
Time period = 13 Years
Interest rate during first 7 Years = 5%
Interest rate after 7th Year = 3.8% p.a Convertible bi monthly
Computation of Accumulated value at the end of 7th Year
We know that Future Value = Present Value ( 1+i)^n
Here I = Rate of interest and n = No.of Years
Future Value = $ 4715( 1+0.05)^7
= $ 4715( 1.05)^7
= $ 4715*1.4071
= $ 6634.48
Hence Balance after 7 Years is $ 6634.48
Computation of Accumulated amount at the end of 13th Year
The amount $ 6634.48 Becomes principal amount now
Time period left = 13-7 = 6 Years
We know that Future Value = Present Value ( 1+i/6)^6n when interest is Compounded bi monthly
Here I = Rate of interest and n = No.of Years
Future Value = $ 6634.48( 1+0.038/6)^6*6
= $ 6634.48 ( 1+0.006333)^36
= $ 6634.48( 1.006333)^36
= $ 6634.48*1.255183
=$ 8327.49
Hence accumulated value after 13 Years is $ 8327.49
If you are having any doubt,please post a ccomment.
Thank you.please rate it.