A person opened an account on April, 2011 with a deposit of 800.The account
paid 6% interest compounded quarterly. On October 1 2011 he closed the account and added
enough additional money to invest in a 6 month time-deposit for 1,000, earning 6%
compounded monthly.
(a) How much additional amount did the person invest on October 1?
(b) What was the maturity value of his time deposit on April 1 2012?
(c) How much total interest was earned?
Answers
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(a) Additional amount the person invested on October 1 = Rs. 175.82
(b) Maturity value of his time deposit on April 1 2012 = Rs. 1030.40
(c) Total interest was earned = Rs. 54.58
Step-by-step explanation:
(1+ i )^n = 1.03022500 for i = 3/2 %, n = 2
(1+i)^n = 1.03037751 for i = 1/2 % and n = 6
Initial deposit of Rs. 800 for 6% compounded quarterly.
P = 800
m = 4
I = i/4 = 0.06/4 = 0.015
N = mn = 4 * 0.5 = 2
Amount = P (1 + I)^N
= 800 (1 + 0.015)^2
A = 824.18
So excess amount invested to reach Rs. 1000 = 100 =- 824.18 = Rs. 175.82
Now Rs. 1000 is deposited
P = 1000
m = 12
I = i/12 = 0.06 / 12 = 0.005
N = nm = 12 * 0.5 = 6
Amount = P (1+I)^N
= 1000 (1 + 0.005)^6
= 100 (1.0304)
A = Rs. 1030.40.
Total interest earned = 24.18 + 30.40 = Rs. 54.58
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