Question

8 -12 points HarMath Ap1263.043 MI. out the end of each buntil the account with teat 50,000 ( d ter duary o the nearester) (a) How long s what will the contribution at the end of (1) Supe when the account reaches $150.00, the business owner total value of the ind your tester 15 more w

Answer 1

Investment = $ 4,000 at the end of each quarter

Interest rate = 6% compounded quarterly

Future worth = $ 150,000

$\large FW = A(F/A,i\%,n)$

Plug in the values given

$\large \implies 150,000 = 4,000 \times \frac{1.015^n -1}{0.015}$

$\large \implies \frac{1.015^n -1}{0.015} = \frac{150,000}{4,000}$

$\large \implies 1.015^n -1=0.015 \times 37.5$

$\large \implies 1.015^n = 0.5625 + 1$

$\large \implies n log(1.015)= log(1.5625)$

$\large \implies n = \frac{log(1.5625)}{log(1.015)}$

$\large \implies n = 29.97$

Number of quarters = 30

B. In the question it is asked that after the 30 quarters when account balance is $ 150,000 the deposit rate has been doubled to $ 8000 and we have to determine the future value after 15 more years.

$\large FW = A (F/A,i\%,n)$

Here, A = $ 8,000

Interest, i = 1.5% per quarter

Time = 15 years = 60 quarters

$\large FW =150,000(1+0.015)^{60} + 8,000 (F/A,1.5\%,60)$

$\large \implies FW =366,482.9663 + 769,717.2137$

$\large \implies FW = \$ \ 1,136,200$

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