Answer to Question #269437 in Financial Math for sumu

Question

Deepika deposits $10000 into her savings account that earns 7% per annum

compounded annually for first two years, 8% compounded semi-annually for next three

years and 12% compounded quarterly for the last two years.

(i) Find the accumulated amount at the end of the first five years.

(ii) Find the accumulated amount at the end of seven years.

b) Pathum deposits 100000 rupees which compounded annually with interest rate i per

annum. If the total amount doubles after 6 years find the value of i. (Hint: Use the

formula R = P(l + i)t )

Answer 1

(i) At the end of two years Deepika will have $10000*(1+0.07)^2=$ 11449$

The this amount begin to raise 8% compounded semi-annualy for the next 3 years, so at the end of that time it will be

$11449*(1+{\frac {0.8} 2})^{\frac 3 {0.5}}\approx14486$ $

(ii) Then this value (12878$) begin to raise 12%compounded quarterly for the next two years. So, at the end of this time(7 years in total), there will be

$14486*(1+{\frac {0.12} 4})^{\frac 2 {0.25}}\approx 18350$ $

(b) $R = P(1 + i)^t$ , where R - total sum after t additions, i - interest rate, t - number of additions, P - initial sum

In the given case we have

$2P=P(1+i)^6\implies(1+i)^6=2\implies 1+i=2^{\frac 1 6}\implies i=2^{\frac 1 6}-1\approx0.122$

Interest rate is approximately 12.2 percent per annum