Question

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

Answer 1

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

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