1. A bank gave John a $5000 loan that he has to repay in 5 years at an annual si
ID: 1134472 • Letter: 1
Question
1. A bank gave John a $5000 loan that he has to repay in 5 years at an annual simple interest rate of 10%. How much interest does John pay for this loan and what is the total amount due at the end of the loan?
2. You deposit $100 in an account Earning 5% for 4 years.
After 4 years the value in account is
A.–$121.55
B.$121.55
C.$121.67
D.$431.01
E.None of the above
3. If your savings can provide 0.25% interest per month, how much do you need to save today to have $6000 in 3 years?
A.5955.22
B.5490.85
C.5484.20
D.2070.19
4. A credit card’s APR is 12% with monthly compounding
What is the effective interest rate?
A.12.00%
B.14.4%
C.4.095%
D.12.68%
Much Thanks!
Explanation / Answer
Answer
1)
Simple Interest Rate Formula is given by:
Simple interest(SI) = P*r*T, where T is time P is initial amount (i.e. Principle) and r is interest rate(Note that If interest rate is 3% then r = 0.03.
In the case P = 5000, T = 5 and r = 10/100 = 0.1
so Simple interest(SI) = 5000*0.1*5 = $2500
Hence Amount due = P + SI = 5000 + 2500 = $7500
2)
The correct answer is (B) $121.55
Amount if compounded annually = P(1+r)T , where T is time P is initial amount (i.e. Principle) and r is interest rate(Note that If interest rate is 3% then r = 0.03.
Hence in this case.P = 100, T = 4 and r = 5/100 = 0.05
Amount = 100*(1 + 0.05)4 .
Hence Amount = 121.55
Hence, The correct answer is (B) $121.55
3)
The correct answer is (B) $5490.85
Interest rate per month = 0.25% hence Annual interest rate= 0.25*12 = 3
Using formula discussed above in part 2) But in this case We have amount = 6000, T = 3 and r = 0.03 and we have to calculate P(initial value of Present value)
Amount if compounded annually (A) = P(1+r)T
=> A = 6000 , T =3 and r =3/100 = 0.03.
Hence,
Value that we have to save today (P) = A/(1+r)T = 6000/1.033
= 5490.85.
Hence the correct answer is (B) $5490.85.
4)
The correct answer is (D) 12.68%
In order to find APR we have to find the interest rate that the amount earned is worth amount when interest rate is 12% complounded monthly,
Amount if compounded monthly (A) = P(1+r/12)12*T
Hence r = 0.12/12 = 0.01, T = 1.
So Amount if compounded monthly(A) = P(1+0.01)12
Hence we have to calculate R such that
P + PRT = P(1+0.01)12, Note that T = 1
Hence P + PR = P(1+0.01)12
=> R = 1.0112 - 1 = 0.1268 ~12.68%
Hence Annual effective interest rate = 12.68%.
Hence The correct answer is (D) 12.68%
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