On January 30, business woman Hillary takes out a $250,000 loan at 6% annual int
ID: 3030922 • Letter: O
Question
On January 30, business woman Hillary takes out a $250,000 loan at 6% annual interest. The maturity date (the day RR has to pay off the loan) is November 1st.
A. How much will Hillary have to pay on November 1st?
B. Suppose instead of paying off the entire loan on November 1st, Hillary decides to pay $100,000 on April 1st, and $75,000 on July 1st.
C. How much interest did Hillary pay on April 1st?
D. How much of Hillary’s $100,000 payment went to pay off the principal, $250,000?
E. What is the new principal (or how much more does RR have to pay)?
F. How much interest did Hillary pay on July 1st.
G. How much of Ronald Rumps’ $75,000 payment went to pay off the principal?
H. What is the new principal (or how much more does RR have to pay)?
I. How much does owe on November 1st?
J. How much of Hillary’s final payment went to pay off the principal?
K. What is the total amount of money Hillary paid for the loan?
L. How much did she save by making the two partial payments.
Explanation / Answer
a) time = 9/12 = 0.75 yrs. applying compound interest
Amount = principal( 1+ rate/100)^n = 250000( 1+ 0.06)^0.75
= $ 261167.66
Total amount she wouldpay on 1st Nov = $ 261167.66
c) On 1st April , n = 2/12 =0.167 ;
Amount = 250000( 1+ 0.06)^0.167 = $ 252444.60
Interest on 1st April = 250,000 - 252444.60 = $ 2444.60
d) Amount paid as principal = $ 100,000 - $ 2444.60 = $ 97555.40
e) New Principal = $ 250,000 - $ 97555.40 = $152444.60
f) Period between 1st April to 1st July =3 months =3/12 =0.25 yrs
So, Amount on 1st July =152444.60( 1 +0.06)^0.25 = $ 154681.55
Interest on1st July = $ 154681.55 - $152444.60 = $ 2236.95
g) Out of $75000 , principal amount = $75000 - $ 2236.95 = $72763.05
h) New Principal = $ 154681.55 - $ 75000 = $79681.55
i) Now for period between 1st July and 1st Nov = 4 months = 4/12 = 0.33
Calculate amount due on 1 st Nov : Amount = 79681.55(1 +0.06)^0.33
= $81288.55
On 1 st Nov she owe's $81288.55
j) So, Principal she paid on 1st Nov = $250,000 - ( $175000) = $75000
k) Total amount she paid = $ 175000 $ + 81288.55 = $256288.55
l) So, first calculate Amount if she pays full payment on 1st Nov:
Amount = Principal( 1+0.06)^(9/12) = $ 261167.67 .This was the amount due $ 261167.67
So, she saved =$ 261167.67 - $256288.55 = $ 4879.11
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