# math

Henry Devine bought a new dishwasher for 320. He paid 20 down and made 10 monthly payments of 34. What actual yearly interest rate did Henry pay?

using this formula r=2mI/p(n+1)
i got this r=2(12)(20)/300(10+1)=

but i don't know what to do next . can you please show me how to do it and correct me it am wrong.

1. 👍 0
2. 👎 0
3. 👁 262
1. Wow, haven't seen or used that formula in almost 50 years.

I don't think you are substituting the correct values.
First of all since Henry paid \$20 down the actual principal is 300

in r=2mI/p(n+1) m is the possible number of payments per year, in this case m=12
I is the actual interest paid, in this case it is 10(34) - 300 = 40
and n is the actual number of payments
p is the principal

so rate = 2(12)(40)/(300(11))
= .2909 or 29.09%

1. 👍 0
2. 👎 0
posted by Reiny
2. I would say that the rate is 12.5%.

btw, this task is just nonsense

1. 👍 0
2. 👎 0
posted by David
3. He borrowed 300 dollars to buy the 320 dollar washer.(since he paid 20 down)
Using the mortgage payment formula:
payment = principal * r/[ 1-(1+r)^-n]
where r is the monthly rate and n is ten months
34 = 300 *r / [1-(1+r)^-10]
[1-(1+r)^-10] = 8.82 r
1 = 8.82 r + (1+r)^-10
I have to solve that by iteration
table of r versus right side, must be 1
.10 .882 + .386 = 1.26
.09 .794 + .422 = 1.22
.08 .706 + .463 = 1.16
.07 .617 + .508 = 1.12
.05 .441 + .614 = 1.05
.04 .353 + .676 = 1.02
.03 .265 + .744 = 1.01
.02 .176 + .820 = .996
so around r = .025 per month or .3 per year
30%
wicked high
check
pmt = 300 (.025 /(1 - (1.025)^-10) ) ??
= 34.27 close enough

1. 👍 0
2. 👎 0
posted by Damon
4. I guess it doesn't hurt to have one more opinion.

I will try to work from basic principles, where the principal will accumulate over the 10 months, and the payments will accumulate at the same rate of interest, separately. At the end of 10 months, the future value of the principal and the payments should be equal.

Let
P=principal, \$300
r=rate of interest per month, about 0.025
n=number of periods, 10
A=monthly payment, \$34

Future value of the principal
= PR^n

Future value (FV) of the first payment (payable after at the end of the first month)
= AR^(n-1)
FV of second payment
= AR^(n-2)
...
Future value of last payment
=A
Thus future value of monthly payments
=A(1+R+R^2+....+R^(n-1))
=A(R^n-1)/(R-1)

Equating future values,

PR^n = A(R^n-1)/(R-1)
Substituting numerical values:
300R^10=34(R^10 -1)/(R-1)

This can be solved by iteration if we arrange the equation as:

R=(34(R^10-1)/(300(R-1)))^(1/10)
With an initial value of R=1.025, we get successively
R=1.02417
1.02377
1.02359
1.02350
...
and finally
R=1.0234293 at the 8th iteration.
or 2.343% per month, which translates to 1.0234293^12
=1.3204, or
32.4% p.a. simple interest

Check using Damon's formula
monthly payment
= principal * r/[ 1-(1+r)^-n]
=300*.02343/(1-1/1.02343^10)
=34.000
OK

1. 👍 0
2. 👎 0

## Similar Questions

1. ### Math

Henry Devine bought a new dishwasher for \$320. He paid \$20 down and made 10 monthly payments of \$34. What actual yearly interest rate did Henry pay?      A. 68.75 B. 14.55 C. 34.38 D. 29.09 The answer is B?

asked by Tayler on January 14, 2015
2. ### Math

Henry Devine bought a new dishwasher for \$320. He paid \$20 down and made 10 monthly payments of \$34. What actual yearly interest rate did Henry pay?      A. 68.75 B. 14.55 C. 34.38 D. 29.09 My answer is B.

asked by Sarah on January 15, 2015
3. ### math 4

Henry Devine bought a new dishwasher for \$320. He paid \$20 down and made 10 monthly payments of \$34. What actual yearly interest rate did Henry pay? A. 29.09 B. 68.75End of exam C. 14.55 D. 34.38 Please explain to me

asked by zyanna on August 4, 2014
4. ### Math

Henry bought a new dishwasher for \$320. He paid \$20 down and made 10 monthly payments of \$34. What actual yearly interest did Henry pay? 1 - 14.55 2 - 29.09 3 - 34.38 4 - 68.75

asked by Kate on December 14, 2007
5. ### Algebra 1

The marketing director of a department store interviewed 50 customers who had bought appliances the previous week. They found that 20% of the customers bought a washing machine and 40% bought a dishwasher. Also 48% of the

asked by Sharon on May 14, 2014
6. ### math

Pam bought a new bedroom suit for \$2588.she made a down payment of \$188 and paid the remaining amount in 24 equal monthly payments.How much did she pay for each monthly payment? 188-24=164 is that how to do it? PLEASE REPLY BACK

asked by breyona on October 1, 2014
7. ### Math

Joe bought a television for \$286.26, including tax. He made a down payment of \$50.00 and paid the balance in 6 equal monthly payments. What was Joe's monthly payment for this television? A\$41.04 B\$39.37 C\$44.38 D\$31.04

asked by Katie Hairston on June 16, 2016
8. ### math

Joe bought a television for \$286.26, including tax. He made a down payment of \$20.00 and paid the balance in 6 equal monthly payments. What was Joe's monthly payment for this television?

asked by nicky on February 11, 2016
9. ### math

An article can be bought for cash at \$20,000.00. A customer bought it on hire purchase by paying a deposit of 20%. An interest of 10% was charged on the remaining balance and he was required to pay the balance in 15 monthly

asked by Lindsay on November 9, 2012
10. ### math

A newlywed couple bought a washer and dryer for \$800. They paid 5% down and then paid 12 monthly payments of \$65.41. Determine the APR of the loan to the nearest tenth of a percent.

asked by Jennifer on June 24, 2014

More Similar Questions